Jiyoung Ha_thesisbook 2018_MFA

New type of gallery typology; Toward Ephemeral space, Liberating place/White Cube for space by Jiyoung Ha

Š2017 Jiyoung Ha

A thesis submitted in partial fulfillment of the requirements for the degree of Master of Fine Arts in Interior Design School of Design Pratt Institute 1 /Ha

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Contents

01 a. Problems / Needs, White cube?

Content; Art / art industry Solution _ Instant Gallery 02 b. Spatially, Model study _ positive/negative Presedents _ space boundary 03 Design exploration/Form Study 04 Design Phase Infinite Periodic Minimal Surfaces Without Self-Intersections 05 3 CASE STUDIES Aa Bb Cc 06 Citation

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a.

Problems / Needs ,

movement could not speak out further than its own boundary, as its boundaries is more static than its desires.

Limited gallery business model.

Segregated structure between major and minor galleries, and the art contents major galleries want are very specific which is that

Art and interior design are the artists have already achieved reputable following. Most major supporting segregation in a way.

And I believe there is the way we galleries in New York are located in expensive neighborhoods can provide certain services for Medicine Ave, Soho / Tribeca, and the public. Art history has shown Chelsea. An economical result of many attempts to go outside of the “White cube” for liberating art the high rent is the hesitatation to invest in unproven artists/art. from limitations; limitation of a view of art, limitation of medium of art, limitation of how art should be Social structural problem.

Industry is run by the privileged presented in gallery space, and people, the hierarchy environment limitation of the role of viewers.

For instance, installation art differs of art society: gallery, academic factionalism, etc. from traditional media in that it addressed the viewer directly as

Here is a good case that a literal presence in the space. adress this issue of the institutionRather than imagining the viewer alized.

NEA established its Artas a pair of disembodied eyes that in-Public-Places(AiPP) program survey the works from a distance, in 1967.

NEA policy emphasizes installation art presupposes an the dissemination of and access embodied viewer whose senses to art experiences regardless of of touch, smell and sound are any perceived social barriers, and as heightened as their sense of the agency of culture’s receivers; vision. providing the individual with an

However, a major limiting opportunity to make an educated hinderance for art liberation is that choice about having high quality art in one’s life. Thus the endowart only describes this issue for ment often finds itself straddling its own sake/ satisfaction. This

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expectation for high culture and hopes for populist appeal in an effort to provide quality art for everybody.

How about the spacial quality?

Public deserves quality spaces.

“White cube”; generic white washed static gallery space – limitations: orthodox ideas.

It is been used as generic bleached out gallery space which is purposely designed for disconnecting the past and the real world.

b.

Spatially,

from all those concerns.

While looking at the playground design, children are totally exposed to the outside. There are no walls to protect them from the nature and no single act (program) to be performed for using the space. They are climbing,

People tent to believe physical division, the “White wall”, sliding, swirling, and engaging with a space more than any other makes a space.

However, I believe that the sense enclosures. As diverse mediums of being in space is created when to interpret the world develop, the perception of space is changing. a thing/object/person Space doesn’t need to obey funcand a thing/object/person interacts with each other. Every object tions anymore. Now, program and has both intensive and extensive materiality are no longer deterministic when programs find the need properties. Space between soft to be flexible and revitalized. chiffon fabric and hard concrete, Maybe, architecture should have there is a narrative. This seflexible forms of presentation as quence of objects’ invisible aura, void space, or the consequences well. So, I wanted to create spontaneity and to explore non-static, of reactions is created by us, self-explanatory, interactive, liberspace designers. al, and vulnerable space/system (soft architecture).

If “White wall” is not the only option for creating a division or making a space, what other forms of boundaries can define a space?

People believe that shelter (architecture) protect them from the nature by creating a layer, a wall, between nature and human being. People try to exert control over nature while professing keywords such as waterproof, UV-resistant, and earthquake resistant.

I disagree that people can be free

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Martini, Pietro Antonio, Exposition au Salon du Louvre en 1787, 1787. Wildenstein Institute, Paris.

Early American Room, Museum of Fine Arts, Boston, Mass. Image via the Library of Congress

a+1. White Cube Charlotte Klonk said. “At the same time, the Nazis also mobilized the traditional connotation of white as a colour of purity, but this played no role when the flexible white exhibition container became the default mode for displaying art in the museum.�

MOMA

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WHITEWALL

BAUHAUS INTERIOR

WHITE CUBE

O’Doherty identifies the transition in question as modernism bringing “to an endpoint its relentless habit of self definition.”

The defining of self means the purposeful neglect of all that is other than self. It is a process increasingly reductive that finally leaves the slate wiped clean. modern gallery space ;“constructed along laws as rigorous as those for building a medieval church.”

“The outside world must not come in, so windows are usually sealed off. Walls are painted white. The ceiling becomes the source of light. The wooden floor is polished so that you click along clinically, or carpeted so that you pad soundlessly, resting the feet while the eyes have at the wall. The art is free, as the saying used to go, “to take on its own life.”

The white cube was a transitional device that attempted to bleach out the past and at the same time

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control the future by appealing to supposedly transcendental modes of presence and power. But the problem with transcendental principles is that by definition they speak of another world.not this one. It is this other world, or access to it, that the white cube represents. It is like Plato’s vision of a higher metaphysical realm where form, shiningly attenuated and abstract like mathematics, is utterly disconnected from the Life of human experience here below.

Hito Steyerl

Robert Irwin

NEW ART

Anish kapoor

Sol LeWitt Bourriaud claims “the role of artworks is no longer to form imaginary and utopian realities, but to actually be ways of living and models of action within the existing real, whatever scale chosen by the artist.�

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Banksy

PUBLIC ART public art in Ancient Greece is the Parthenon (c.447-422 BCE)

INTERACTIVE ART 1950 Marcel Duchamp Gordon Matta-Clark

DADAISM 1915 Marcel Duchamp

VIDEO ART 1960 Nam June Paik Hito Steyerl

PROCESS ART 1960 Jackson Pollock

STREET ART 1970-80 Banksy

ENVIRONMENTAL ART / LAND ART 1960-70 SITE-SPECIFIC-ART INSTALLATION INTERACTIVE ART + TECH 1970 1970 1970 Rafael Lozano-Hemmer Sol LeWitt RELATIONAL ART 1990

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Character of new comtemporary art

CONVENTIONAL MEDIUM

PERFORMATIVE NEW ART FORM

action

painting

artist

reaction

artist Characteristic of new art.

Interactive with the outside Dematerialization of the art object Abandonment of conventional mediums

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world

the thing specific object

Ecosystem_problem in art industry consumer public

consumer rich-people

residence

consumer public major gallery

gallery ONLY WAY

museum gallery art fair residence

gallery

GAP

art biennial

artist residence

NEW MODEL’S GOAL create more overlap of PUBLIC + RICH PEOPLE break one way path new artist / public liberalization art

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Problem solving _in urban context

Urban context “A City Is Not a Tree,” Lefebvre repeated several times that a city with a tree structure leads to social segregation.138 For Lefebvre, as for Alexander, the reductionism of functionalist urbanism stems not from a scientific analysis but rather from the tendency of the designers to give up the more complex structures of traditionalcities, characterized by the experience of overlap, ambiguity, multiplicity.

small gallery art biennial

small gallery residence

artist

art fair museum

small gallery

ONLY WAY major gallery

residence

consumer public

consumer rich-people

“Diagram of Human Relationships in the City,” reproduced in Lefebvre’s review of the project in Revue française de sociologie

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According to Lefebvre, structured city is reinforcing a social segregation. The art ecosystem structure is shown the same pattern that “Diagram of Human Relationships in the City” had. In the city context, it needed to create “Spontaneity and Self-Organization”. Furthermore, how powerful our public pocket spaces; vacant space, unrecognized space, can be if we’re given the opportunity to interactivewith and share more with one another. People can explore the city in different scales.

“Through the RedBall Project I utilize my opportunity as an artist to be a catalyst for new encounters within the everyday.

Through the magnetic, playful, and charismatic nature of the RedBall the work is able to access the imagination embedded in all of us. On the surface, the experience seems to be about the ball itself as an object, but the true power of the project is what it can create for those who experience it.

It opens a doorway to imagine what if?

City Pocket space Medicine ave chelsea

soho / tribeca

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For the CITY, Spontaneity Self-Organization Informal public spaces | Stairway Cinema by OH.NO.SUMO. Housed in a corner in Auckland, this mini movie theater outdoor aims to recreate a space of socialization and communication projecting short films from the Internet.

Instant Gallery

Q How could we share more memories about our abandoned building and gaining the better understanding of landscape?

How can we neglected space became a constructive one?

How powerful our public spaces can be if we’re given the opportunity to interactive with and share more with one another.

The result is participatory: We create open platforms of exchange that welcome transformation and reinterpretation,

Mission Finding Pocket Space in the city!

Medicine ave

Chang, Candy. Before I die. St. Martins Griffin, 2013. using neglect space with a simple tool

chelsea

Location Artist Genre Address

soho / tribeca

Instan t Galle ry

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current situation google

One, provide business model for young artists/galleries.

Two, enhance the new type of art (non-static or non-traditional) Three, Give public back an opportunity to make an educated choice about having high quality art in one’s life.

b.

Spatially,

ing a space, what other forms of boundaries can define a space?

Space doesn’t need to obey functions anymore. Now, program and materiality are no longer determin People believe that istic when programs find the need shelter (architecture) protect them to be flexible and revitalized. from the nature by creating Maybe, architecture should have a layer, a wall, between nature flexible forms of presentation as and human being.

People try to well. So, I wanted to create spon People tent to believe exert control over nature while taneity and to explore non-static, physical division, the “White wall”, professing keywords such as self-explanatory, interactive, libermakes a space. waterproof, UV-resistant, and al, and vulnerable space/system However, I believe that the sense earthquake resistant. (soft architecture). of being in space is created when I disagree that people can be free a thing/object/person from all those concerns. and a thing/object/person interacts with each other. Every object While looking at the playground has both intensive and extensive design, children are totally exposed to the outside. There are properties. Space between soft no walls to protect them from the chiffon fabric and hard concrete, nature and no single act (prothere is a narrative. This segram) to be performed for using quence of objects’ invisible aura, void space, or the consequences the space. They are climbing, sliding, swirling, and engaging of reactions is created by us, with a space more than any other space designers. enclosures. As diverse mediums to interpret the world develop, the If “White wall” is not the only option for creating a division or mak- perception of space is changing.

Space

Q

one direction

Art

multi direction

As diverse art content develops, the perception of the white wall is changing.

Can we create a new frame for art? Why are gallery walls static?

Art movements are changing to capture the time toward flexible forms of presentation, reconsideration of the visitor’s role and physical presence is very active.

If the contents are less static, should space also transform from the static concept of the white cube?

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POLE COLUM BOUNDARY WALL

SPACE

GRID GUID LINE

_ 01

HOW CAN WE SHaPE THE SPACE?

SPACES

PACE

SPACES PACE

SPACES

PACE

SPACES

PACE

Wht if people can visualize the space inbetween? between pole to pole, wall to wall, object to object? Consider the grid is the system give the “SI” system stardart to measure the space SI Systems of natural units (such as Planck units) are useful in theoretical physics, but are not suitable for everyday purposes; because the SI units are defined in terms of constants of nature they can be thought of as natural units rescaled to human proportions.

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positive space

negative space

POLE COLUM SPACE

BOUNDARY WALL

GRID GUID LINE

SPACES

PACE

01

01

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SPACES PACE

SPACES

PACE

SPACES

PACE

02

02-03

03

04

04

Front/ postive space Back/ nagative space

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01

02

03

Inside out- dynamic time is moving.

layer of Inner spaces

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04

Case Study

Presedent Research 20 /Ha

2017 Fall Thesis INT 799a Jon Otis Jiyoung Ha

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occupied space circulation semi/unoccupied

precedents

experimental fields for aesthetics.

Both invite non-professionals and insiders, children and adults to use them as laboratories in order to give their thoughts and movements free rein to experience new Why should an art museum things, test out the unknown, and Noguchi organize an exhibition about play- enter into relationships. They may ground? I am convince that the be niches but their subversive pospace recognition/boundary two can learn a great deal from tential is not to be underestimatThe components of a Noguchi one another and are fundamentaled. Viewer’s awareness of how playground may always be experily similar in nature.Both develop objects are positioned in a space, enced by the children in multiple their potential as clearly defined and of our bodily response to this. ways. Instead of directly suggestfree spaces, as public places and The components of a Noguchi

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ing a single act to be performed (sliding, climbing, swinging), these projects require kids to engage with a space, to explore and subvert it.

playground may always be experienced by the children in multiple ways.Instead of directly suggesting a single act to be performed (sliding, climbing, swinging), these projects require kids to engage with a space, to explore and subvert it.

“to ensure that users would be have the freedom to alter the spaces to meet different needs within a reasonably short time period, it began to make more sense to me to pursue flexibility in the relations between adjoining places, and in the way various spaces are connected with each

precedents junya ishigami: KAIT kanagawa institute of technology Architects: Junya Ishigami + Associates | Junya Ishigami Profile Location: Kanagawa, Tokyo, Japan Program: Educational Architecture / University Site area: 129,335m2 Total floor area: 1,989.15m2 Structure: Steel frame Maximum height: 5,052mm

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other.’ says junya ishigami.” the resulting free-forming room both blurs its edges between the numerous internal programs, and also the connection between the inside and outside world. a total of 305 pillars are dotted throughout, with differences in size and shape

they reference the irregular nature of tree trunks, evoking the sense of wandering through an unknown forest.

ture, art and design. The program of exhibitions, artists talks, film screenings, conferences and publications is intended to generate dialogue and collaboration across geographic, ideological and disciplinary boundaries. As a public forum for emerging voices, Storefront explores vital issues in art and architecture with the intent of increasing awareness of and interest in contemporary design.

precedents STOREFRONT FOR ART AND ARCHITECTURE New York, United States 1993 PROGRAM: facade renovation for art & architecture gallery CLIENT: Storefront for Art and Architecture STATUS: complete Storefront for Art and Architecture is a nonprofit organization committed to the advancement of innovative positions in architec-

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In 1992, Steven Holl and artist Vito Acconci were commissioned as a collaborative team to renovate the aging facade of the Storefront for Art and Architecture.

The Storefront for Art and Architecture is situated on the corner of a block that marks the intersection of three distinct neighborhoods: Chinatown, Little Italy and SOHO. The gallery itself is a limited, narrow wedge with a triangulated exhibition interior, such that the most dominant structure for the Storefront for Art and Architecture is the building’s long facade.

Seeking to introduce improbability and to puncture the facade, Acconci and Holl challenged this symbolic border which underlines the exclusivity of the art world, where only those on the inside belong. Using a hybrid material comprised of concrete

mixed with recycled fibers, Holl and Acconci inserted a series of hinged panels arranged in a puzzle-like configuration. When the panels are locked in their open position, the facade dissolves and the interior space of the gallery expands out on to the sidewalk.

If the function of a facade is to create a division separating the inside from the outside space.

01 02 03 04 01_ intimate space 02_ personal space _ 1.5ft 03_social space_4ft 04_public space_12-25ft

precedents The Hidden Dimension Edward T.Hall A chart depicting Edward T. Hall’s interpersonal distances of man, showing radius in feet and meters.

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01

PLAY WORK BUILD WASHINGTON, D.C.

An exhibition offers investigation of the history of construction toys and block play. Children and families can experience the National Building Museum’s unique Architectural Toy collection with Rockwell Group’s groundbreaking play space,

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02

-

scale

Imagination

Actuality

+

increase perception & learning

precedents

Imagination Playground.the relations between adjoining places, and in the way various spac

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Research _

Precedents

Art Fair/ Biennial different type of gallery Six sided modules increase the average wall area and enhance views into and from the main circulation areas.

It offers “a more articulated path that encourages discovery” creating “a much more exciting public space.” conclusion Limitation Gallery; mostly loft condition, empty space with no design aspect for new type of art Art fair; mostly rectangular equally distributed space. Typical white-cube setting

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Rafael Viñoly’s Structural Experiment at Park Avenue Armory

Isamu noguchi On the limited square foo tage of the stage, Noguchi was able to explore space, figuration and the social and emotional interactions of people through sculpture, using the physical boundaries of the stage in a kind of life-size experiment.

“It had within it all the elements of space perception, of the volume of space, not just two-dimensional space but the three-dimensional space of the theater. My interest was to see how sculpture might be in the hypothetical space of theater a living part of human relationships. That was my particular interest and always remained so.” _ Noguchi Make the dancers awkwardly aware of the bed’s unconvention-

al design, forcing them into odd positions.

ON

OVER

IN

UNDER

Precedents TESSERACTS OF TIME - A DANCE FOR ARCHITECTURE Steven Holl, 2015 Eric Hawkins in ‘Stephen Acrobat’ photographed

by Philippe Halsman. Set Design by Isamu Noguchi.

1946.

isamunoguchi’s set elements for martha graham dance company’s production seraphic dialogue, 1955, brass rods and steel cable | ph by kevin noble | via thenoguchimuseum: hawktrainer

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The first section ‘UNDER’ begins with a slow movement of sunlight coming from above, sweeping across the curved interior spaces of the architecture.

The dance physically vibrates in the dark shadows of the stage.

Dancers are dressed in black geometric and angular costumes.

Their movement is grounded and driven with linear thought to the percussive score Anvil Chorus by David Lang.

For the second section ‘IN’, compressed spatial sequences filled in deep light are projected in film. The dance movement defies gravity and explores geometry with emotional expression.

Space and body in black and white work in synchrony with the minimalist piano music Patterns in a Chromatic Field by Morton Feldman.

The third section ‘ON’ -all in white- reveals on stage three twelve-foot-tall Tesseract Fragments. In geometry, the tesseract is the four-dimensional analog of a cube. In dance, the movement explores space now present in the 3rd dimension of the stage. The music is percussive, prepared piano The Perilous Night by John Cage.

The fourth section ‘OVER’, begins with the tension of sound and energy as the Tesseracts rise upwards to the music Metastaseis by Iannis Xenakis. Unlike the previous sections, bursting color floods the stage with dancers in asymmetrical colors of oranges and reds. Arvo Pärt’s Solfeggio takes shape in a synthesis of chromatic forms as the dance releases like a sunrise into intensely lyrical and hypnotic meditative phrases.

on necessity, in other words, a search for architecture of Metabolism is suggested.The upper structure was fully prefabricated and it took only 6 days to build the whole five-storey structure including the floors, windows, roof, and tower. Steel pipe units play a main role in this work. Twelve curved steel pipes are attached to each other to form a cross horizontally and vertically. A steel panel is welded to the curved part that is a center of the cross, turning pipes into a unit.

Case study Suita, Osaka, Japan Design: Construction: 1968 - 1970 Site Area: 1,000m² Building Area: 298m² Total Floor Area: 1,237.6m² Structure: Steel Structure 1 Basement Stories + 4 Stories

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Design Concept: The four-floor framework of the upper structure is composed of steel pipes, forming. It forms a tree structure stretching out in all directions.This structure is characterized with its potential to extend, or replicate horizontally and vertically depending on necessity.

An investigation of structure, whether a structure can expand, shrink, or reduce depending

Case study R. Buckminster Fuller.

Geodesic dome, spherical form in which lightweight triangular or polygonal facets consisting of either skeletal struts or flat planes, largely in tension, replace the arch principle and distribute stresses within the structure itself. It was developed in the 20th century by American engineer and architect

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Artwork: There’s more than one way to balance the weight of a building. Instead of chaneling it through heavy vertical walls and horizontal floors, Richard Buckminster Fuller’s famous geodesic domes distribute force evenly through an outer “skin” of interconnected triangles. This creates an uninterrupted interior space much more cheaply and using much less material. As he pointed out in his 1954 dome patent, you need 23kg (50lb) of wall and roofing material to shelter 900 sq cm (one square foot) of floor space, but you can achieve the same end with only 0.35kg (0.78 lb) of geodesic dome. That works out at abut 600 times less building material! Furthermore, Fuller claimed his domes were strong enough to withstand winds of 240 km/h (150mph). Artwork courtesy of US Patent and Trademark Office from US Patent 2,682,235: Building Construction by Richard Buckminster Fuller, published June 29, 1954.

on their logical, self-explanatory construction principles. Their flexibility and modularity offer freedom of design. Reduction and clarity in form are our guiding principles in the aesthetic design. They are esteemed worldwide and have been honored with the highest awards.

Product research Flexure: The Flexible Wonder Toy The system’s wooden dowels follow a Fibonacci 2-3-5 pattern. https://www.kickstarter.com/projects/1891653500/ flexure-the-flexible-wonder-toy?ref=live

“I wanted the pieces to innately lead to non-block forms, to literally lead to out-of-the-box building,” says Elaver. “I specifically avoided 90-degree angles, and with Flexure it’s easier to make a hexagon than a square.”

“Structures like those designed by Frank Gehry and Zaha Hadid cannot be made with traditional building blocks,” says Elaver. “They are based on flexible, dynamic mesh models—a moveable grid of non-rectangular elements.”

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stopper

Product research

weight

72 90 120

180

Burkhardt Leitner modular architectural systems for temporary structures in the trade fair and display, office and public space, museum and exhibition fields.‫‏‏‬Our main activities include the development, the design and the product communication of the individual components and their complex construction, the production of these architectural systems and their worldwide distribution via sales, planning and license partners. The high functionality of our architectural systems is based

exsisting products’ limitation is it only can achieve a curve when the size is big enough to make a curvature. even tough joint system has various directions, but line (pole) has one direction, so it leads centrosymmetric shape only. You can see possible applications. Smart joinery system, portable, easy to install, self-explanatory product, Lighting and hanging systems applications.

Product research Stick-lets After months of research, field study, and prototyping, I realized that the tool should be open-ended, simple, portable, AND fun. It should trigger a direct relationship with nature by giving children the freedom to manipulate, construct, and design their own experiences.

Since classic toys such as building blocks are still a big hit; why not take the free play outside?

Stick-lets help children of all ages get back outside to create engaging and memorable experiences.

By using Stick-lets, kids fall in love with the resourceful, renewable, and plentiful element: the stick! These durable, reusable, weather-resistant and safe silicone joints stretch the imagination through the simple act of lashing

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together various sizes of scavenged sticks.

The flexible nature of the six shapes gives kids the freedom to build forts, toys, animal kingdoms, geometric shapes, and much more. Stick-lets promote problem-solving, team building skills, imaginative dexterity,

design discovery and hands-on learning through physical manipulation (i.e. built with your own two hands!).

-Christina Kazakia, Creator

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Form Study

Design exploration

Design exploration_Form study shrink /expand = scaling metamorphosis = transforming state variable = adapting liberal space

close

open +

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-

scale + Intimacy -

01

02

03

05

04

Form study Martha Graham (May 11, 1894 – April 1, 1991) was an American modern dancer and choreographer. Her style, the Graham technique, reshaped American dance and is still taught worldwide Graham technique is based on “contraction and release”, and uses different parts of the body in opposition to one another to create spirals for dramatic tension.

It also incorporates formal exaggerations of “natural” movements

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Performed to music by Zoltán Kodál y, Lamentation premiered on January 8, 1930, at New York's Maxine Elliott'sTheatre.

01 02 03

04 05

shaping the motion

01

02

03

04

05

Echappe a ballet movement in which the dancer jumps from the fifth position and lands on the toes or the balls of the feet in the second position.

04

01

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02

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05

m l

a

p

n k j o c

b

i e d

g

f

h

Situation exsisting products’ limitation is it only can achieve a curve when the size is big enough to make a curvature. even tough joint system has various directions, but line (pole) has one direction, so it leads centrosymmetric shape only. joints system embracing non-centrosymmetric shape c

a

j k

b e d

f

g

a o

aim for non-centrosymmetric shape a joint has different directional points

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l

i h

m

n

o

p

street

subway

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d

Douglas Gordon

c

b

a surface

a top view

d a

Possible application case 01

Douglas Gordon (Scottish, b. 1966)

visualizes, pictures, and “sculpts” time in many of his works.

In 1993, Gordon presented a version of Alfred Hitchcock’s film Psycho, projected onto a translucent screen and slowed down to a duration of twenty-four hours.

Gordon’s 24 Hour Psycho, which is included in this exhibition, marked the beginning of the artist’s ongoing method of altering, monumentalizing, and alienating viewers’ common understandings of the moving picture. Douglas Gordon: Timeline focuses on the film-related work of his oeuvre and his direct references to Andy Warhol, Alfred Hitchcock, Martin Scorsese, and other cornerstones of film history.

The exhibition ranges from a large-scale projection of an elephant in Play Dead (2003) and direct references to Andy Warhol’s Sleep (1963) in Film Noir (Perspire) (1995) to the phenomenon of superimposed visuals in Between Darkness and Light (After William Blake) (1997).

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c Anthony McCall

a

b

light scenario

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42 /Ha 2017 Fall Thesis INT 799a Jon Otis Jiyoung Ha

Design Phase Infinite Periodic Minimal Surfaces Without Self-Intersections

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2017 Fall Thesis INT 799a Jon Otis Jiyoung Ha

Infinite Periodic Minimal Surfaces Without Self-Intersections

demonstrated in their Scientific Graphics Project that for the TPMS P, G, D, and also for a fourth surface (I-WP) of genus 4, there is a striking connection between the skeletal graph of the surface and a modified version of its level surface approximation. Perhaps similar matches will be found for other examples Infinite Periodic Minimal Surfaces Without Self-Intersections of TPMS, including surfaces of genus greater than 4.

In a 1970 NASA Technical Note Infinite Periodic Minimal Surfaces Without Self-Intersections (p.38 ff), described how skeletal graphs can be used to represent TPMS. More recently David Hoffman and Jim Hoffman (no relation) have

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A minimal surface is a surface that locally minimizes its area! having a mean curvature of zero!

x=(u,v,h(u,v)) therefore satisfies Lagrange`s equation _ In mathematics, a minimal surface (1+h(v)^2)*h(uu)-2*h(u)*h(v)*h(uof revolution or minimum surface v)+(1+h(u)^2)*h(vv)=0 of revolution is a surface of revolution defined from two points in a half-plane, whose boundary is the axis of revolution of the surface. It is generated by a curve that lies in the half-plane and connects the two points; among all the surfaces that can be generated in this way, it is the one that minimizes the surface area.A basic problem in the calculus of variations is finding the curve between two points that produces this minimal surface of revolution. A minimal surface parametrized as Minimal surface

P ‘P’ stands for primitif, the name assigned long ago by German crystallographers to crystal structures that have the symmetry of a packing of congruent cubes. The P surface exhibits this symmetry. Each of the two congruent interpenetrating labyrinths into which space is partitioned by the P surface may be regarded as an inflated version of the skeletal graph with tubular edges that enclose the edges of a packing of congruent cubes. The symbol for the space group of P (No. 229) is Im3′m. (Alan Mackay, the British physicist and crystallographer, has wittily dubbed P ‘the plumber’s nightmare’.)

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(No. 224) is Pn3′m. P and D contain both embedded straight lines and plane geodesics. A straight line in either surface morphs into a plane geodesic (a mirror-symmetric plane line of curvature) in the other surface. Because every straight line embedded in a minimal surface is an axis of 2-fold rotational symmetry, a half-turn about the line switches the two sides of the surface and D also switches the two inter-pene‘D’ stands for diamond. The trating labyrinths into which space congruent pair of skeletal graphs is partitioned. A TPMS is called of its labyrinths are dual diamond balanced if its labyrinths are graphs , whose edges correspond congruent. P and D are both balto the bonds between adjacent anced surfaces. carbon atoms in diamond. The symbol for the space group of D The Weierstrass integrals shown G ‘G’ stands for gyroid, a name I chose to suggest the twisted character of its labyrinths, which — unlike the labyrinths of P and D — are opposite mirror images (enantiomorphs). The skeletal graphs of G are dual Laves graphs. The symbol for the space group of G (No. 230) is Ia3′d.

below define the rectangular coordinates of P and D and of countably many associate surfaces. θ is called the angle of associativity or Bonnet angle. For θ = 0, the equations describe D, and for θ = π ⁄ 2, they describe P. D and P are called adjoint (or conjugate) surfaces.

Model A Gyroid BCC _ BODY CENTERED POINT

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01. ISO VIEW _ BCC 02.diagram_ understanding nature of geometry

create shape

wrapping a fabric around the poles

a point holding a structure

basic modular box setting

weight point

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B A

01. ISO VIEW_ assmebld Gyroid model C

ISO

AB

C

02. ISO VIEW_ explode Gyroid understanding its weight point, connectivity and possible shape that can create by assembling each sell.

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01. ISO VIEW_ By controling the apeture of geometry, users can customize the degree of privacy and amount of interior/exterior conditions they need.

02. SECTION VIEW_ mid points distance from edge index A_ 1 B_1.5 C_2.13

A

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B

A

B

C

scale variation _ possible scenario

01. 6set

02. 4set

03. 4set

04. 2set

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15

4set

6set_ dance stage

1,350

1 90

Stage Size: 45’wide x 30’ deep Cast: 13-17

03. Iso view

Dimension

Floor material

Black/Grey marley

02. Floor plan

01. Rendering view

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2set_stage

01. Rendering view

03. Iso view

02. Floor plan

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4set_outdoor movie theatre 01. Floor plan

02. Iso view

03. Rendering view

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Model B FCC _ FACE CENTERED POINT

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.001

.11/ .46/ .24

.70/ .00/ .97

.00

ab

de

.27/ .88/ .15

.69/ .09/ .34

.17/ .33/ .11

.15/ .05/ .63

c

f

01. X+/ Z / Xthree points the each index defines the shape of membrane (face ) in

04.

Shape of face Z direction is mainly controlling The indoor quality of the space defined by fabric

02. z point

c

b a e

03. shape of face

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d

out

f

C

A joint

B

face

control pole

C

B A frame

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B A

rendering

system

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scale variation _ possible scenario 01. large 8set

02. mid 5set

03. small 2set

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Rendering view The difference between a mega form and megastructure has to do with how flexible the formal system is in accommodating multiple hands or authors over time.

The mega form tends to be authored by a single individual ( or team), because its structure is not organize in a schematic way that can accommodate a multiplicity of hands as a project evolves over time. The megastructure is much more systemic and allows for such evolutionary collaboration. ...It allows for multiple authors and multiple hands tobe able to build it over time.

The question then turns to the range of control between the larger morphology and the authorship of the individual pieces.

Manfredi, Michael A., and Marion Weiss. Public natures: evolutionary infrastructures. Princeton Architectural Press, 2015.

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mid 5set

while the space empty, when the space done with its job people finds shades around this pavilion. people can define its functionality

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small 2set Liberating art, Create new frame/ stage for the art on the street. Every art should be valuated equal ly.

It could be the street version of White cube or deconstructive white cube

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Categorized users / possible functions to apply Ballet hippop Public space

Public art

Hito Steyerl

Indoor

out door

ex) subway

ex) park, street, under a bridge and par k

dance performance art

dance performance art

video art installation arti

Kusama yayoi

nstallation art

music performance artm

Douglas Gordon

usic performance art

clasic

audio

lighting

strip lighting

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face/privacy

membrane fabric

acoustic proof

wool panel

floor

Black/Grey marley

jazz

Aa Active engagement Walking through

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Bb Passive engagement walking around

Indoor condition

Outdoor condition

Projection

Lighting / IlluminationS 64 /Ha

Mounting

ound

joinery itteration study

Model A Model B

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indoor_ outdoor_Frame option Fabric display

Frame

form making

Reinforce structure Power Lighting

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Sound

Sound quality

kevlar

Kevlar maintains a more constant dispersion pattern at all frequencies in its range and transmits far fewer delayed, time-smearing sounds to the listener.

Not only does it deliver a cleaner sound, it can do so to a wider group of listeners.

convex

http://www.bowers-wilkins.com/Discover/Discover/ Technologies/Kevlar.html

sound traveling sound source

Relection

concave concave 67 /Ha

48”

4”

2”

YAMAHA VXL1-24, VXL1-16, VXL1-8

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Lighting / Illumination

Lighting quality Power source

power

Honda EU2200iTA1 Companion Inverter Generator

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night Lighting up art pieces 70 /Ha

morning

Mounting

Mounting quality

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B

C

A

C

A B

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Detail Drawing

section

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Joinary studies

reinforce structure with frame connection detail

frame with face control connection detail

modelB joinary system drawing

modelB joinary system

joinery extract process diagram

modelB joinary detail system drawing

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modelB joinary detail system drawing

4 3 2-2 2-1 1

JOINERY top rotation variation front+top+right

front+top

4 3 2-2 2-1 1

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front

4 3 2-2 2-1

1 JOINERY right rotation variation

front+top+right

front+top

front

2-2

4 3 2-1 1

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4 3

2

1 JOINERY front rotation variation

front+top+right

front+top

front 4 3 2-2 2-1 1

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T

Joinery Form

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full 1,2-1,2-2

F

R

full / 2(1peice) 1,2-2,3 .

1 1

Soft architecture is based on the computer system, which creates various thinking methods of architecture design and architectural forms. To be specific, architectures can be self-evolutionary and adaptive to the humans’ behavio rs by optimizing the inner organization and physical structure.

Does this show the soft architecture itself an architectural machine? Buildings do not predict people’s behaviors either, but the building is able to feedback and define people’s behaviors mutually, as humans are reconstructing buildings all the time, which might be the predictability that belonging to an architecture and makes building a machine.

Space quality that I achieve is the idea; Dilute the vertical division. White wall could be flexible, soft material blur the boundary between interior/exterior, place/space and horizontal/ vertical. The space people find the comfort or function is not “inside” not the space protected by a concrete wall.

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.00

Step 01 play with tool kit tool

b _ shape

1.00

.11/ .46/ .24

a _ configuration

.70/ .00/ .97

a

.27/ .88/ .15

d

.17/ .33/ .11

b

.69/ .09/ .34

e

Step 04 chose your site! check site package

c

.15/ .05/ .63

f

Site City, Public Pocket space Space really is for people.

Wall is an obstruction and allege People orchestrate space.

M. Paul Friedberg

01. X+/ Z / Xthree points the each index defines the shape of membrane (face)

01

02. z point

c

b

02

a e

03. shape of face

SiteA

f

subway_ Port authority passway next to N,Q,R line 01 landscape view 02 grid condition 03 material condition long white wall (subway tile) green steel grid frame 04,05 perspective view

d

Step 02 check your options

04

scale variation

scale variation

02 01

_ possible senario

01. 6set

_ possible senario

05

01. large 8set

02. 4set

street

02. mid 5set

03

03. 4set

SiteB

park_ Highline below the bridge 01 sky view picture 02 grid condition 03 perspective view

03. small 2set

04. 2set

SiteC

Broadway-Lafayette St

Step 03 check your possible materials / functions and contruction method.

C

01 perspective view 02 grid condition 03 material condition

Categorized users / possible functions to apply

A joint

long white wall (subway tile) navy painted steel grid frame 04,05 perspective view

Ballet hippop

Public space

B

Hito Steyerl

Douglas Gordon 01

face

Public art

Indoor

out door

ex) subway

ex) park, street, under a bridge and park

dance performance art

dance performance art

video art

Kusama yayoi

installation art

installation art

music performance art

music performance art

clasic control pole

audio

lighting

face/privacy

acoustic proof

floor

C

B A frame

strip lighting

B A

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membrane fabric

wool panel

Black/Grey marley

jazz

03

27/ .88/ .15

17/ .33/ .11

b

e

.69/ .09/ .34

Step 04 chose your site! check site package

c

.15/ .05/ .63

f

Step 05 we will do render for you! check your space.

Site City, Public Pocket space Space really is for people.

Wall is an obstruction and allege People orchestrate space.

M. Paul Friedberg

fines the shape of membrane (face)

01

c

b

02

a e

SiteA

f

subway_ Port authority passway next to N,Q,R line 01 landscape view 02 grid condition 03 material condition long white wall (subway tile) green steel grid frame 04,05 perspective view

d

04

05

mid 4set

02 01

system

ge et

rendering

The result is participatory: We create open platforms of exchange that welcome transformation and reinterpretation,

street

d et

03

SiteB park_ Highline below the bridge 01 sky view picture 02 grid condition 03 perspective view

Step 06 promote your gallery with app

mall et

SiteC Broadway-Lafayette St 01 perspective view 02 grid condition 03 material condition long white wall (subway tile) navy painted steel grid frame 04,05 perspective view

Instant Gallery

Medicine ave

Ballet hippop Hito Steyerl

Douglas Gordon 01

Location Artist Genre Address

Mission Finding Poket Space in the city!

Kusama yayoi

chelsea clasic

03

jazz

soho / tribeca

current situation google

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Instant Gallery

One, provide business model for young artists/galleries.

Two, enhance the new type of art (non-static or non-traditional) Three, Give public back an opportunity to make an educated choice bout having high quality art in one’s life.

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Aa Bb Cc

3 CASE STUDIES

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2017 Fall Thesis INT 799a Jon Otis Jiyoung Ha

Graphical (2d-mentional) Colorful Lighting design and Costume are separated There is no Set designer involved.

Graphic is the main medium to engage with the contents.

Case Aa Artist Site 84 /Ha

The Oculus The new port of entry to Lower Manhattan, Westfield World Trade Center is located at the site where 60,000 neighborhood residents, 300,000 daily commuters, 13 subway / PATH trains, multiple ferry lines, and an additional 15 million annual global travelers converge within one landmark setting.

This new New York City experience brings together commerce, community and culture in a destination integrating the Santiago Calatrava’s designed Oculus, street-level space in WTC Towers 3 and 4, as well as the galleries that run underground across the World Trade Center campus (including to 1 WTC, now the tallest building in the Western Hemisphere).

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Program This Oculus allows natural daylight to flood into the WTC Transportation Hub; filtering down through all levels eventually to the PATH train platform, approximately 60 ft below the street. At night, the illuminated building will serve as a lantern in its neighborhood. Santiago Calatrava speaks of light as a structural element in the WTC Transportation Hub, saying that the building is supported by ‘columns of light.’

Time

8-9

10-12 place to rest

1-25 play

3-4 place to rest

natural light

-6 play artificial light

36’ 9’

9’

27’

approximately 350' long, 115' across at its widest point and rises to a height 96' above grade at its apex.

resting spot place to appriciate the space!

Running Time: 40 minutes Cast: 13 dancers: 6 men, 7 women Recording should be played through a stereo or 6 channel sound system.

Live Music: 4 or 5 musicians.

Scores and instructions included in the dance capsule.

To beperformed through a 6 channel sound system.

Stage Size: 45’ wide x 30’ deep. 6’ additional upstage of dance area for décor.

Audio: Recorded music: stereo playback, PA system Live music: 8-channel sound system, Kyma system, laptop, multichannel audio interface, 6 DI boxes

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Circulation

Tower 2

indirect path direct path prime zone secondary zone

Subway

Subway Path hall

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FL plan The transportation Hub is defined by a series of steel ribs arranged in a large elliptical shape. The space between every rib is transparent and allows natural light to flood transit hall. In addition, the HUB looks like a glowing lantern at night, its light illuminating the adjacent streets. The column-free space underneath is approximately 111 meter long and 43 meter wide. Above ground level, the ribs extend vertically, connected to two 107 meter long arches. Between the arches, a 100 meter long skylight allow you to see the sky and One World Trade Center.

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Existing condition

36’

sound 36’ 15

1,350

48’ 1 90

Dimension

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Stage Size: 45’wide x 30’ deep Cast: 13-17

Sound effect

are usually called satellite units.

The arrangements of a 5.1 surround sound setup shown in the picture below. prefered audio distance audio

5.1 Surround Sound Systems 5.1 Surround sound systems are one of the widely used surround sound setup in home theater systems.

Usually- Dolby Digital and DTS encoded in a DVD are 5.1 channel audio formats.

5.1 surround sound technologies produces five channels 350’ of sound in the left, right, center, left-surround and right-surround positions. These five channels are the minimum required to produce 5.1 surround sounds. The dot decimal (.1) represents the channel for LFE (low frequency effects), which is usually sent to a subwoofer. Other 5 units are capable for handling the frequency range except low frequency(Usually they are capable of handling the frequency range from 100Hz to 22Khz and no need for any other higher frequency component like tweeter). These five units

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suggestion zone for sound quality

36’ 9’

9’

27’

approximately yg350' long, 115' across at its widest point pg and rises to a height 96' above grade at its apex.

9’

Lighting effect

Scenario for day

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Scenario for nigt

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Cultural Hub Possiblity of indoor large setting Relatively protective environment_ curating more_ sound/lighting Backdrop color is white_ enhance visual ability

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Case Bb Artist

Overlay with mutiple media strong/ vivid color

Site SOJUNG KIM mixmedia artist Through strong radiant colors, hypnotic patterns, and biomorphic forms, my work expresses emotional experiences that are both pleasing yet overwhelming.

This level of high stimulation asks viewers to become aware of their body’s perceptual and physical responses to the intense reflections of light and color.

I communicate through forces that are instinct, while activating desires that drive the subconscious.

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Subway

Chelsea

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Madison Square Park Our Mission is to protect, nurture, and enhance Madison Square Park, a dynamic seven-acre public green space, creating an environment that fosters moments of inspiration.

As stewards, we strive to engage the community through our beautiful gardens, inviting amenities, and world-class programming. We believe that in an urban setting everyone deserves access to a park that allows for recreation, respite, and reflection Be Surprised By Our Art There’s nothing more striking than the juxtaposition of art and nature. You’ll see plenty of both in Madison Square Park.

Since 2004, Mad. Sq. Art has commissioned and presented over thirty world-class installations in Madison Square Park by acclaimed artists ranging widely in practice and media.

Porocity diagram Expanding Art from Chelsea; growing art movement Supporting art Gathering environment Inviting people to interact with art; co-exsisting art with life/ function Providing shades at park

shadow

sun

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FL Plan 36’ 9’

9’

27’

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sun

openness

Porocity diagram

shadow

N

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section view

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Rendering

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Case Cc Artist Site

Woody Vasulka early pioneers of video art, and have been producing work since the early 1960s.

The couple met in the early 1960s and moved to New York City in 1965, where they began showing video art at the Whitney Museum and founded The Kitchen in 1971. Steina and Woody both became Guggenheim fellows: Steina in 1976, and Woody in 1979.Woody began making independent documentaries and edited industrial films at Harvey Lloyd Productions. In 1967, at the request of architects Woods and Ramirez, Woody collaborated on developing films designed for a multi-screen environment to be shown in the American Pavilion at Expo 67 in Montreal. In 1968

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The Kitchen is a non-profit, multi-disciplinary art and performance space located at 512 West 19th Street, between Tenth and Eleventh Avenues in the Chelsea neighborhood of Manhattan, New York City.

High Line User & Use Analysis About 3 million people visit the High Line per year, making the park one of the most tourist and visitor oriented parks in the world. People enjoy picnic, walked hand in hand, read their books, lying on the lawn, sunbathing and socializing.

Different people come up here will feel different things and have a different set of experiences. site image

“ new and still retain the old.”

Size The first section of the High Line Park is 2.88 acres and over 0.5 miles long, which runs from Gansevoort Street to West 20th Street.

The second section which is also 0.5 miles long, runs from 20th Street to 30th Street, while the third section runs from 30th Street to 34th Street.

The High Line Park has width of 30–50 ft and depth of 18–24 inches and is 18-30 ft high. It has a total length of approximately 1.5 miles and a total surface area of 753,500 sq ft.

Gallery

Commercial Museum

Museum Residence Commercial Gallery Residence

Shade environment _ projecting video Intimate space_ theatre atmosphere Match with artist’s color _ Woody is based in Chelsea area Galleries area _ bring high-end art to outside of white cube

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FL plan/ Zoning / circulation

passive zone pre- active zone

Gallery area

active zone display viewer path general path

Retail area

Wihtney Museum High Line

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Activity diagram 23’ 3/4” 23’ 6”

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Activity diagram

Bright

Dark (under bridge)

b

b

a

c installation area active view

c

a

passive view

Dark

Bright

eating

waiting

watching

n one, whteis g ar

performing

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Activity Spectrum

enjoying

passing

Structure diagram

Display zone ; projection needed high traffic floor material enclose space

power

structure supporting frame

frame integrated w models

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structure suporting frame designated by form / function

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Citation ODoherty, Brian. Inside the White Cube: the Ideology of the Gallery Space. University of California Press, 1999.

Corner, James, and Alison Hirsch. The Landscape Imagination. The Collected Essays of James Corner, 1990-2010. Princeton Architectural Press, 2014.

Bloemink, Barbara. Design Life Now: National Design Triennial 2006. Smithsonian, 2006.

Moussavi, Farshid, and Michael Kubo. The Function of Ornament. Actar, 2008.

Gordillo Bárbara Asnaghi. Zumthor: Arquitectura Para Un Lugar = Architecture for a Place. Departamento De Proyectos Arquitectónicos ETSAB-UPC, 2013.

Zumthor, Peter, et al. Thinking Architecture. Birkhäuser, 2015.

Griffith Winton, Alexandra. “The Bauhaus, 1919–1933.” In Heilbrunn Timeline of Art History. New York: The Metropolitan Museum of Art, 2000–. http://www.metmuseum.org/toah/ hd/bauh/hd_bauh.htm (August 2007; last revised October 2016) Diller, Elizabeth. “Two Thoughts.” Log, no. 10, 2007, pp. 49–38. JSTOR, JSTOR, Stanek, Łukasz. “Research: From Practices of Dwelling to the Production of Space.” Henri Lefebvre on Space: Architecture, Urban Research, and the Production of Theory, NED - New edition ed., University of Minnesota Press, 2011, pp. 81–132. JSTOR, Armijos, Samuel J. Fabric architecture: creative resources for shade, signage, and shelter. W.W. Norton, 2008.

Hall, Edward T. The Hidden Dimension. Peter Smith Pub, 1992.

Kwon, Miwon. “One Place after Another: Notes on Site Specificity.” October, vol. 80, 1997, pp. 85–110. JSTOR, JSTOR, www.jstor.org/stable/778809.

Reiss, Julie H. From Margin to Center: the Spaces of Installation Art. MIT Press, 2001.

Kennedy, Daniel P. et al. “Personal Space Regulation by the Human Amygdala.” Nature neuroscience 12.10 (2009): 1226–1227. PMC. Web. 27 Oct. 2017.

“A person’s personal space is carried with them everywhere they go. It is the most inviolate form of territory” Richmond, Virginia (2008). Nonverbal Behavior in Interpersonal Relations. Boston: Pearson/A and B. p. 130. ISBN 9780205042302.

“The genesis of an idea… the point of departure for all my subsequent theatre work: space became a volume to be dealt with sculpturally.” _ Isamu Noguchi, A Sculptor’s World (New York; Harper & Row, 1968), 125.

“Research: From Practices of Dwelling to theProduction of Space.” Henri Lefebvre on Space: Architecture, Urban Research, and the Production of Theory, NED - New edition ed., University of Minnesota Press, 2011, pp. 81–132.

Lamentation Ballet choreographed by Martha Graham. Online Text. Retrieved from the Library of Congress, <https://www.loc.gov/item/ihas.200182679/>.

Manfredi, Michael A., and Marion Weiss. Public natures: evolutionary infrastructures. Princeton Architectural Press, 2015.

Poling, Clark V. “Design Issues.” Design Issues, vol. 3, no. 1, 1986, pp. 87–89. JSTOR, JSTOR, www.jstor.org/stable/1571645.

Johnston, Pamela, et al. The Function of the Oblique: the Architecture of Claude Parent and Paul Virilio 1963 - 1969. AA Publ., 1996.

INFINITE PERIODIC MINIMAL SURFACES WITHOUT SELF-INTERSECTIONS Alan H. Schoen Electronics Research Center Cambridge, Mass.

Johnston, Pamela, et al. The Function of the Oblique: the Architecture of Claude Parent and Paul Virilio 1963 - 1969. AA Publ., 1996.

Nicola D. Ridgers, Laura M. Carter, Gareth Stratton, Thomas L. McKenzie; Examining children’s physical activity and play behaviors during school playtime over time, Health Education Research, Volume 26, Issue 4, 1 August 2011, Pages 586–595, https://doi.org/10.1093/her/cyr014 Chapter 4: Calculating Fractal Dimensions, www.wahl.org/fe/HTML_version/link/FE4W/c4.htm#box. ndanos, Author. “Tag: Triply Periodic Minimal Surface.” WeWantToLearn.net, wewanttolearn.wordpress.com/tag/triply-periodic-minimal-surface/.

Davis, Ben. “László Moholy-Nagy’s Miss at the Guggenheim.” Artnet News, Artnet News, 27 June 2016, news.artnet.com/exhibitions/laszlo-moholy-nagy-guggenheim-exhibition-507140.

“What Do Lighting and Set Designers Do?” DanceTabs, 3 Mar. 2013, dancetabs.com/2013/02/what-do-lighting-and-set-designers-do/.

Leung, Nick. “Shapes, Fractals, Time & the Dimensions They Belong To.” WeWantToLearn.net, 28 Oct. 2017, wewanttolearn.wordpress.com/2017/10/18/shapes-fractals-time-thedimensions-they-belong-to/.

“Isamu Noguchi.” CAITLIN PONTRELLA, 8 Jan. 2016, www.caitlinpontrella.com/new-blog/2016/1/12/isamu-noguchi-playscapes.

Tate. “White Cube – Art Term.” Tate, Tate, www.tate.org.uk/art/art-terms/w/white-cube.

Cain, Abigail. “How the White Cube Came to Dominate the Art World.” Artsy, Artsy, 23 Jan. 2017, www.artsy.net/article/artsy-editorial-white-cube-dominate-art.

“Hilbert’s Curve: Is infinite math useful?”, 3Blue1Brown, YouTube, Published on Jul 21, 2017, https://www.youtube.com/watch?v=3s7h2MHQtxc&feature=share “Fractals are typically not self-similar”, 3Blue1Brown, YouTube, Published on Jan 27, 2017, https://www.youtube.com/watch?v=gB9n2gHsHN4 “Thinking visually about higher dimensions”, 3Blue1Brown, YouTube, Published on Aug 11, 2017 https://www.youtube.com/watch?v=zwAD6dRSVyI Chang, Candy. Before I die. St. Martins Griffin, 2013.using neglect space with a simple tool

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