Universal Haircutting Method (UHM)
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Journal of Orthocouralogy
No. 8
and Associated Disciplines !
Haircutting Architecture and Hairstyling Design Art and Logic
The OFHE/OFBE "The Ortho-Fundamental Haircutting/Building Element: A breakthrough paradigm brings logic and a new dimension to haircutting instruction." H1
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Master Program
ORTHOCOURALOGIST
November 26th 2014
Patrick F. Garelle
Universal Haircutting Method (UHM) No. 8
Haircutting Architecture and Hairstyling Design Art and Logic
Master Program
ORTHOCOURALOGY 6
OFHE/OFBE/ortho-prism . The OFHE base (1) is theoretically considered to be spherical. . The true geometric segment-cut (SC) is not indicated here since it is hidden between the holding fingers.
ORTHOCOURALOGY Patrick F. Garelle Patrick F. Garelle
Journal of Orthocouralogy and Associated Disciplines !
Haircutting Architecture and Hairstyling Design Art and Logic
Orthocouralogy or The Scientific Method of Haircutting "The Journal of Orthocouralogy and Associated Disciplines" (JO-AD) will be a publication introducing a new discipline: the formal, academic study of the art, method, technique of haircutting, designated by the term "orthocouralogy." This journal aims towards the dissemination of research findings which are scientifically based, in order to improve both professional and teaching performance in the field. Such scientifically designed methodology had previously been regarded as undefinable by many or eagerly awaited by others. Overdue, then, since the early years of the 20th century, "JO-AD" should cause a significant turnaround. It is intended for all professionals, salon owners, manufacturers, and enterprises with interests in this flourishing field. STRATEGY involves two main stages of dissemination. The first involves publication of existing haircutting theories and commonly held technical beliefs, along with challenges to those assumptions. In the second stage, unlimited publication of articles dealing with non-technical aspects, such as political or legal ones, would serve as a platform or forum for investigators. BREAKTHROUGH adapts mathematics to the system of haircutting. Art is translated into science in several logical and explicit chapters. A new philosophy for instructing and also practicing is put into place. Some major institutions in the beauty industry, as well as professors, doctors, librarians, and trained stylists have already been receptive. "The creation of orthocouralogy is revolutionary and should change the way haircutting is learned...This program boosts the level of education way up." MANDATE constitutes the need to review and reform and re-analyze the validity of all previously held standards. Orthocouralogy and the journal, "JO-AD," invite a thorough, serious investigation of professional regulations on all levels, including cosmetic licensing. This will prove to be essential for all existing and potential students. Such reform is imperative and inevitable.
Š Copyright 2014 Patrick Garelle international corp ALL RIGHTS RESERVED
August 21014
No. 8
Universal Haircutting Method (UHM)
Haircutting Architecture and Hairstyling Design Art and Logic REVIEW, REFORM, and RE-ANALYZE
Images taken from the Orthocouralogical Fundamental Haircutting Elements Table
ORTHOCOURALOGY ORTHOCOURALOGY ORTHOCOURALOGY
ORTHOCOURALOGY Patrick F. Garelle Patrick F. Garelle
Patrick F. Garelle
Orthocouralogical Fundamental Haircutting/Building Element
O.F.H.E/O.F.B.E The adaptation of mathematics based on empirical observation (explained in issue No. 1), which led to the description and definition of temporary structures of hair use to give haircut might very well be the most important theoretical and practical breakthrough in haircutting education. Without this invention, orthocouralogy truly could not exist, much less attain the level of sophistication it has at present. It seems to make sense that without the use of mathematics, the rationalization, logical explanation, and creation of haircutting systems was not possible. It is also believed that the rational discourse made possible by the use of elementary math marks the end of intuitively-directed haircutting education. The use and adaptation of mathematics is indeed the only way to give rational technical explanations, which make it easier to teach the art of haircutting. Observing and trying to figuring out the logic of haircutting procedures which have never been properly explained is simply impossible. One of the engineering concepts is to provide students with the necessary technical knowledge to help accelerate the development of fine motor skills, and to give them the technical tools that will allow them to express themselves artistically, rather than to learn the style of someone else who cannot teach it correctly. Obviously, orthocouralogy in its essence is not an artistic class, although it is strongly believed that it will ultimately increase the realization of artistic potential. Journal No. 8 represents a brief introduction of the OFHE, which is perhaps the most important founding document of orthocouralogy. Theories such as those mentioned below were founded on the particular purpose, analysis, and physical properties an OFHE, or series of OFHEs. Theories: . time for giving a haircut . technical quality . motion quality . haircutting dimensions (2nd or 3rd) . recording the infrastructure of a haircut . transmitting how a haircut is given . creating a haircut . formalization/standardization of haircutting instruction
ORTHOCOURALOGY Patrick Patrick F. F. Garelle Garelle
Without a clear understanding of the effects those different groups of hair can have on the technical qualities of a haircut, practical performance levels and knowledge levels can’t be evaluated correctly. Without the research introduced in this journal, progress in the art of haircutting education is not possible. The amount of information delivered in JO-AD No. 8 is a limited representation of the research made on this particular subject. ORTHOCOURALOGY People who don’t have a specific plan of action prior to giving a haircut, who proceed intuitively until they lock on something that could look good, are those most likely to make technical mistakes. Many hairstylists begin to give a haircut without knowing exactly what they are going to do, and more importantly without knowing or understanding the fundamental technique(s) they are using. August 29th 2007 "Note: The mathematical content presented 2736 × 3648 5.8 MB 3,266 of 12,214 herein is intended for theoretical and illustrative
purposes. It is not intended as actual mathematical instruction and has not been reviewed by mathematicians."
ORTHOCOURALOGY
ORTHOCOURALOGY
We felt it was important to assign a meaningful name to designate what is one of the most important and fundamental structural elements used in giving haircuts. Knowledge of what an OFHE/OFBE is is more fundamental than knowledge of fundamental haircut designs. Why? Assuming the responsibility for teaching someone to cut hair, knowing that that person’s intention is to make a living using that education, necessitates the understanding of the most fundamental elements of haircutting. In French-speaking countries, these groups of hair selected by hand and comb are called “mèche” (translation: wick). Other European countries use the expression “design line” or “artistic guideline,” which only refers to the tip or apex ridge of that temporary manmade hair structure. In Asia, such as in Japan, the term for a selected group of hair translates to “bundle” or “bunch.” In the U.S., no specific term other than “guideline” was employed until we created orthocouralogy. It is a matter of historical fact and record that no better or more meaningful name has ever been applied to these temporary formations of hair, which may be of many different shapes and therefore consistently categorized and typed. The reason may be that no one before has thought or observed that it was possible to do so. I found it particularly strange that no significant name was ever given to the most fundamental element used in giving haircuts; but after all, haircutting has mainly been approached as an art rather than a science (although many people would like it to be both). Since the beginning of the modern era of technical haircutting (circa 1914 to the present), most hairstylists have used and still use the technique of selecting successive groups of hair to give the best haircuts they can. Great haircut designs resulting from this technique have become fashion trademarks in almost every decade of the 20th century, and still, no one ever thought of giving the simple group of hair the name it deserved.
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Why not?
OFHE with a slanted ridge/segment-cut (SC)
ORTHOCOURALOGY
Ortho-triangular face
Ortho-quadrilateral face
ORTHOCOURALOGY Patrick Patrick F. F. Garelle Garelle
Presentation of the OFHE (in brief) OFBE: General definition and description (based on the simplified assumption that the head is spherical and only positively curved - see figure: G10 page 9) An OFHE can be defined geometrically as a temporary, three-dimensional semi-solid or figure made of a group of hair (and empty space/air) specifically organized for the purpose of giving a haircut. An OFHE can be used to reduce the volume of a hair mass in a specific manner. The use of OFHEs can be considered the simplest and most ingenious technique invented by human beings, to give the greatest number of haircut designs in the most precise way. An OFHE is a specific temporary structure made of a selected group of hair strands, and is used to: ! . give a haircut ! . verify (check) a haircut ! . analyze a haircut. The shape of an OFHE can be geometrically defined as a casual irregular polyhedron or casual prism. The base face of an OFHE is spherical, given the reasonable (if oversimplified) assumption that the surface of the human scalp is spherical. A typical OFHE is considered to have six faces (others can have five or more than six). • The first face is theoretically considered to be a spherical polygon, and formally considered as the number one face. It is also named the “surface of origin face (SO).” • That No.1 face has all its edges curved and typically is quadrilateral. • Typically, but not always, that No. 1 face is considered to be a spherical ortho-quadrilateral face, which ortho-quadrilateral can be of different types, such as spherical square, spherical rectangle, or spherical rhombus). An OFBE is considered as being an irregular ortho-geometrical figure. The OFHE apex is considered the number six face. That sixth face is also called the segment-cut (SC; see JO-AD issue No. 6) OFBEs are formally classified by categories and types. Elaboration The lateral shapes (ortho-triangles or ortho-trapezoids) give the OFBE its orthocouralogical type name. As an example, an OFBE can be formally typed/classified as an orthocouralogical isosceles trapezoid prism when its lateral faces are casually compared with a isosceles trapezoid.
ORTHOCOURALOGY Patrick F. Garelle Patrick F. Garelle
Why Ortho-Prism? Due to its resemblance to a geometric prism in three-dimensional Euclidean geometry but also having spherical geometry properties, an OFBHE is often casually referred to as an “ortho-prism” out of respect to the field of mathematics, simply because it is not actually a prism. The prefix “ortho-” from the word orthocouralogy is used in the abbreviated expression “orthoprism.” The term “prism” is borrowed from mathematical language. An ortho-prism is therefore appropriately considered as a casual prism since it is not prism as formally defined in mathematics. However, in the domain of orthocouralogy, the appellation “ortho-prism” is considered acceptable pending further investigation. Remark: A chain of OFHE/OFBEs or ortho-prisms (orthocouralogical chain) is composed of at least two OFHEs.
The resemblance to a polyhedron A polyhedron (from Greek poly- meaning "many" and -hedron meaning "face") is a solid with flat faces. Each flat surface (or "face") is a polygon. So, to be a polyhedron there should be no curved surfaces. A standard ortho-prism (ortho-polyhedron) can be considered to have six faces. Its base (at the scalp/surface of origin) is formally but simply seen as spherical, therefore curved. Only the other faces are generally considered flat unless originating from the hairline, and not all the faces have straight edges. Four faces are considered ortho-quadrilateral, each having theoretically one curved edge (curvature of the scalp as assumed). One face (the apex/segment-cut) is theoretically considered quadrilateral. An ortho-polyhedron/ortho-prism/OFHE/OFBE is considered to be geometrically irregular.
Why “temporary semi-solid”? The structural formation of an OFHE is considered temporary because it must be held to be formed, and when released it takes a different shape.
O Figure plate G10 positive curve R original drawing 2006 T
ORTHOCOURALOGY Patrick Patrick F. F. Garelle Garelle
H O C O U R A L OG Y
Classification of OFBEs (in brief) The classification of OFBEs by categories and types Only two categories of OFBEs (triangular, trapezoidal), used for different purposes and levels of technical instruction, are presented in this JO-AD. Other categories, such as conic, are defined by orthocouralogy but not addressed in this particular journal.
Utilization Understanding the multiple technical values of the OFBEs is crucial to mastering the technical aspect of haircutting, whether a plan of action is predetermined or not. Understanding what drives the choice of a specific set of OFBEs (action plan), which type of OFBE to use, what size (individual OFBE), the effect of each OFBE, and where to use a certain type of OFBE represent the main concerns in maximizing haircutting control, precision, and accuracy. • Understanding the OFBE’s multiple technical values makes ortho-freestyle haircutting safer. • The use and adaptation of mathematics enables haircutting instruction to be formalized and standardized. • In practice, the types of OFBEs intended for use in a haircut are approximated, not measured or rigidly adhered to. In other words, good judgment must also be exercised. • As a backup, a verification system exists to confirm that the type or types of OFBEs used are appropriate for a desired result. • OFBEs can be represented correctly/accurately on the design/engineering board. Orthocouralogical freestyle haircutting (not to be confused with "general freestyle haircutting") is better executed when the practitioner has clear and full knowledge of the OFBEs’ technical values. One of the exciting things about giving a haircut is giving one that has never been achieved before. Having a creative mind, and engaging in actual haircutting that proceeds from an artistic idea, can sometimes be challenging. • Having the technical knowledge of all elements involved in giving a haircut, and being proficient in the use of that knowledge, ultimately allows heightened artistic performance. • Having technical knowledge and understanding the technical value of all types OFBEs is essential for giving a haircut requiring the use of these elements. • Whether one is conducting a haircutting operation with or without a specific plan of action/blueprint, one needs technical knowledge of the OFBE, and clear understanding that proper physical formation of OFBEs is necessary to maximize the technical quality of haircutting performance. • This knowledge is important when one acts as an instructor, whether one teaches actual haircutting or not. • Having this knowledge adds to the minimum technical procedure for practicing the art of haircutting safely. • Having this knowledge leads to better understanding and use of all haircutting systems.
ORTHOCOURALOGY Patrick F. Garelle
OFBE: Cause and effects behind the logic What permits the mathematical description of these temporary formations made of hair? The visual analysis of these architectural structures, which have been precisely, specifically, and purposely formed, permits the application and adaptation of geometry to describe them. That careful observation allows the definition of faces, edges, and vertices.
What are some advantages of using geometry to describe these temporary formations? • • • • • • • •
It allows for their accurate physical description. It allows the creation of a valid body of educational/academic content. It provides the technical foundation of orthocouralogy. It allows the creation of a technical program that can be graded impartially and accurately. It allows the logical explanation of logical mechanical haircutting systems. It answers the question of whether a logical haircutting method could exist. It allows the development of different levels of technical programs, and fair tests of their knowledge. It allows the development of different levels of practical programs, and fair tests of their knowledge.
We believe it was important to formally name these specifically organized hair formations, since their technical values are vital to giving, teaching, and learning haircutting logically. However, due to the fact that an OFBE is not a true prism according to the rules of geometry, the prefix “ortho-“ (from orthocouralogy) has been added to the expression “fundamental building element/FBE” and formalized for use in the domain of orthocouralogy. Based on fact, there was never a formal or meaningful name for these hair formations of different types, most likely because no one ever thought or observed that it was possible.
ORTHOCOURALOGY Patrick Patrick F. F. Garelle Garelle
In actual haircutting you will have to estimate and use good judgment regarding the type of OFHE you’ll be using. • With time and practice, the type of OFHE you will necessarily use will come more automatically, thus meaning you will not have to think as much about it. • The line of cut (LC) will be the supporting and confirming element that you use to verify that you are on task. Having a good understanding of the expected OFHE type to be used is important at the earliest stage of the learning process. A clear plan of action relative to the haircut design you want to achieve involves having the knowledge of OBHE type you will have to use. OFHE/OFBE variables • category • size • shape/types •
physical properties of hair (e.g., straight, curly, wiry, fine, thick)
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organizational quality
Patrick F. Garelle Patrick F. Garelle
OFHEs/OFBEs chart (incomplete/modified for the JO-AD) ORTO-CELLS TYPES
ORTO-LATERAL FACE TYPES
examples of OFHE Bases/SO (sph-polygons) Assuming the head is spherical all edges can be be considered as arcs. (Since the head is an irregular sphere, some ortho-cells can be different that spherical)
examples of OFHE lateral faces (polygons)
ORTO-QUADRILATERAL FACES TYPES examples of OHBE Front or back faces (polygons)
ortho-triangular and ortho-trapezoidal lateral faces are represented in this type or orthocouralogical table.
ortho-quadrilateral (examples)
SO
O R SO T SO H O SO C SO O U R SO A L OSO G Y
ortho-triangular (example)
ortho-concave polygons
- often resulting form free style haircutting method
O R T H O C O U R A L O G Y
ortho-isosceles triangle
ortho-right triangle
ortho-scalene triangle
ortho-slanted triangle
ortho-rectangular
O R T H O C O U R A L O G Y
ortho-trapezium/trapezoidal (and offset) with slanted SC (irregular)
ortho-rectangular front and back faces with a bent portion (spherical portion)
ortho-rectangular front and back faces
orthorectangular (bent)
ORTHOCOURALOGY
Š copyright 2014
ORTHOCOURALOGY PatrickF.F.Garelle Garelle Patrick
ortho-trapezium/trapezoidal possible front a back face (blue and green)
Segment-Cut (SC) attitude and OFHE/OFBE bases interior angles Ortho-quadrilateral faces only different configurations (ortho-trapezoidal lateral faces omitted) square: right angle with the longitudinal edges
square SCs
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square SC
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slanted SC slanted SC
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slanted SC
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slanted SC
square SCs
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ORTHOCOURALOGY square SC
ORTHOCOURALOGY Patrick Patrick F. F. Garelle Garelle
Shape of ortho-cells
(typical examples)
non-standard ortho-pattern model ortho-cells justification no provided
Construction Section (CS) Transition Section (TS) ortho-cell
ORTHOCOURALOGY
HSED (Haircutting System Engineering Devise)
orthocouralogical non-standard pattern model
ORTHOCOURALOGY Patrick Patrick F. F. Garelle Garelle
Orthocouralogical Fundamental Building Element Categories and Types of Ortho-OFBE/ortho-Prisms (in brief)
Category: Ortho-triangular prism/OFHE (for simplified theoretical instruction and haircutting system graphic design) - ortho-isosceles triangle prism/OFBE - ortho-right triangle prism/OFHE - ortho-equilateral prism/OFHE (questionable) - ortho-scalene prism/OFHE - ortho-slanted prisms/OFHE Category: Ortho-trapezoidal prism/OFBE (for more accurate theoretical instruction and haircutting system graphic design) - ortho-isosceles trapezoid/trapezoidal prism - ortho-scalene trapezoid/trapezoidal prism - ortho-right trapezoid/trapezoidal prism - ortho-slanted trapezoid/trapezoidal prism
Use of good judgment In actual practice, we must be flexible and reasonable about giving the exact geometric shape of any OFBE/OFHE. “Exact� is not going to be possible! For reasons of efficiency and practicality, we are not going to measure with exactitude of any type of OFBE shape. However, on the drawing board (e.g., OrthoTower, or Ortho-Spanish Fan), the representation of OFBE type and ortho-chains made of a type or types of OFBE can be represented accurately. Forming the necessary OFBE type during actual haircutting will have to be done using good judgment and common sense. Constantly monitoring or verifying and analyzing the line of cut (LC) is part of the standard check list procedure. Again, each OFBE has a direct impact on the LC. In other words, we can say that the way we shift each selected group of hair (OFBE) is the way we steer the LC. Furthermore, based upon a specific plan of action for a given haircut design, we can predict and define all types of OFBE necessary to give that specific haircut design.
ORTHOCOURALOGY Patrick Patrick F. F. Garelle Garelle
Having good technical knowledge and being proficient at organizing OFBEs greatly improves technical haircutting performance. Having this knowledge minimizes technical haircutting errors, which in turn greatly limits technical corrections Many haircutting and hairstyling tricks are used by those who have technical or practical issues. Poor technical haircutting performance can be temporarily hidden during the hairstyling phase, unprofessional though this may be. Often, poor technical performance requires a planned or unplanned haircut design to be changed, although minor technical corrections might not necessitate structural changes.
Technical performance quality of OFHE on wet vs. dry hair Generally, we can safely say that all haircut designs that are best given using OFHEs are most efficiently given when the hair mass being treated is wet (not including barbering haircutting technique). In other words, OFBEs are easier to form when the hair is wet. Why? Mainly because dry hair is more difficult to handle, due to the fact that hair is harder when dry as opposed to wet, and therefore more difficult to cut. Dry hair is slippery and therefore less controllable, and consequently is not the most efficient way to analyze the lines of cut. When wet, hair is softer and therefore more controllable, and tends to stick together, which reduces its tendency to slide away from the scissors’ blades as they close. When a segment-cut (SC) is performed on wet hair, that SC is usually cleaner and sharper.
Miami FL, August 16, 20013 DSCF9203 ORTHO-LAB Image taken from the library of orthocouralogy
ORTHOCOURALOGY Patrick Patrick F. F. Garelle Garelle
Naming of the No. 6 Faces of an Ortho-prism Ortho-Polyhedron Ortho-Hexahedron An ortho-hexahedron is an ortho-polyhedron with six faces.
2 ortho-quadrilateral faces - front face - back face 2 ortho-triangular wall faces
The 6th face is the ‘ghost’
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ORTHOCOURALOGY 1 1 ortho-quadrilateral base face/ortho-cell ortho-quadrilateral front & back wall OFHE faces (2 and3), control quantity and shifting mode: (in brief) The front face is made with the new hair to be cut. (in brief) The back face is made of hair already cut. ortho-triangular lateral wall faces (4 and 5): The Faces of an OFHE indicating the shifting type/mode. ortho-quadrilateral base face/ortho-cell: The faces of an OFHE on the surface of origin (SO)/scalp (not always spherical!)
ORTHOCOURALOGY Patrick F. Garelle
Remark: It is the surface occupied by each hair strand’s end cross-section that is considered the added surface/No. 6 (also called the “ghost surface,” since it exists but is not easily visible due to its relatively small size). Defining the shape of that ghost surface simply as ortho-quadrilateral avoids the complications of other possible descriptions. It is also intentional that the ghost surface is usually represented by only a line segment when no fine analysis is needed, simply because the surface is small.
ortho-isosceles triangle or trapezoidal prism/OFHE/OFBE
ORTHOCOURALOGY
ORTHOCOURALOGY Patrick Patrick F. F. Garelle Garelle Patrick F. Garelle Patrick F. Garelle
Rationalization: The making of the theory GENERAL GIVEN THE FOLLOWING MATERIALS AND CONDITIONS • • • • •
A straight pair of scissors (not curved!) A straight comb Mainly the use of holding fingers (usually and primarily the index and middle fingers) Specifically selected group(s) of hair being pulled as straight as possible The use of a haircutting system (not strictly required, but recommended)
RATIONAL APPROACH and DECISION-MAKING PROCESS Based on empirical observations explained in JO-AD Issue No.1, a group of hair specifically organized to cut can be physically seen and described as having a geometrical shape. Based on our prior knowledge of geometry, that shape, carefully and precisely formed in its environment and for its technical purpose, is casually compared to a prism. Because different mechanical haircutting systems and techniques are used to give different categories and types of haircut designs, the idea that different types of prism could be mathematically defined and used made total sense.
Knowledge improves physical and technical performance The size and precision of an OFBE’s formation is dependent on the level of fine motor skills an individual is developing. With practice those fine motor skills usually increase, but not always. Some professionals do remain at a low technical level and don’t see the necessity to improve fine technical performance. Whether these professionals are motivated or not, frustrated or not, the reason is often due to not having enough technical knowledge or understanding of the application and utility of that knowledge. Having a higher level of technical knowledge and a clear understanding of all elements involved in forming and using OFBEs raises the likelihood of good technical haircutting performance. The physical properties of the hair mass (e.g., straight, curly, coarse, wet or dry) can render these formations more or less difficult to make. Having the technical knowledge necessary to better form those OFBEs improves performance.
ORTHOCOURALOGY Patrick F. Garelle Patrick F. Garelle
RESULTS (in brief) The adaptation and use of mathematics to name and define the shapes of specifically organized groups of hair, usable for different technical haircutting purposes, has permitted the development of both a theory of time for giving a haircut and a theory to define the quality level of a haircut.
Other general definitions of an OFHE/OFBE An OFHE/OFBE is defined as a temporary, three-dimensional, semi-solid structure made of hair that is used during a haircut. An OFHE/OFBE can be geometrically seen/described and casually defined as a polyhedron, made of an organized group of hair, usually pulled the straightest way possible and used in giving a haircut. In the most general or broadest sense, an OFHE is a polyhedron having one spherical base -- that is, a face formally assumed to be spherical, although it can sometimes be considered as flat or other, depending on the irregularities of a given human head. This means that the base of an OFHE can be other than spherical. Due to the fact that the human head is not a regular sphere, the adjective “reasonable” and the adverb “reasonably” are often used in orthocouralogical texts.
ORTHOCOURALOGY Image taken from the library of orthocouralogy
ORTHOCOURALOGY Patrick Patrick F. F. Garelle Garelle
FORMAL TERMINOLOGY An OFHE/OFBE considered as casual polyhedron in the domain of orthocouralogy can be referred as an ORTHOCOURALOGICAL POLYHEDRON, or ortho-polyhedron. An OFBE can also be called an orthocouralogical prism, since it presents some similarities to a prism.
INFORMAL TERMINOLOGY The informal expressions “ortho-prism” or simply “prism,” or “ortho-p” or “OP,” are also accepted.
FORMAL COMMUNICATION The prefix “ortho-” and the terms “orthocouralogic,” “orthocouralogical,” and “orthocouralogically” must be used appropriately to avoid confusion with respect to other domains in which the same or similar words may have different meanings.
GENERAL USE OF AN OFHE • •
An OFBE is considered as a haircutting element which is part of an orthomechanical haircutting system. An OFBE can be part of a mechanical haircutting system that is or is not logically organized.
BRIEF DESCRIPTION A typical OFHE is considered to have six faces. • The first face is reasonably considered to be a spherical polygon. That face, formally considered as the number one face, can also be called the surface of origin, or SO, of an OFBE/ortho-prism. • Considered as a spherical face, that No.1 face has all curved edges. • Typically that face is considered (but is not always) a spherical orthoquadrilateral face, which ortho-quadrilateral can be of different types, such as spherical square, spherical rectangle, spherical rhombus (refer to the orthocouralogical table representing the type of ortho-cells). •
The number of straight edges is therefore relative to the number of faces, and the number of curved edges is relative to the base spherical shape.
ORTHOCOURALOGY Patrick Patrick F. F. Garelle Garelle
Why the name Ortho-Prism? Giving more sophisticated haircuts with the idea of maximizing technical haircutting quality has necessitated more precise work. From this objective arose the need to maximize the quality of organization of each selected group of hair strands before cutting. Being more precise and paying more attention to the way I was selecting and configuring these groups of hair gave me a fairly clear picture and made me realize that each of those temporary structures could be physically described in geometric terms. That exciting discovery and realization induced me to push even farther the level of organization, selection, and configuration of these intentional and essential structures. The goal at this point was to justify that geometry could be used to physically define those structural elements that were used to give a haircut in a precise mode. Empirical evidence based on observation indicated that these structures had distinctive faces, edges, and vertices. The evidence these structures occupied space, and therefore could be seen as volumes, led me to identify and compare those volumes with polyhedrons. The only difference from a polyhedron was that one face identified would most likely be spherical. Having made these observations, I could begin to define geometrically all components of those temporary structures. However, I had an issue. I could not call this structure a polyhedron. The problem was that spherical face! Because it did not have all flat faces and straight edges, I could not call it a polyhedron. My respect to all the mathematicians who had invented and developed geometry, particularly Mr. Euclid, prevented me from doing so. My decision was to add the neologism I had invented to define this haircutting method, and create the orthocouralogical polyhedron or ortho-polyhedron. “Ortho-polyhedron� could then perhaps be used a casual geometrical expression for that structure in the domain of orthocouralogy, but also as a formal expression in the domain of haircutting.
The ORTHO-POLYHEDRON becomes the ORTHOCOURALOGICAL FUNDAMENTAL HAIRCUTTING/BUILDING ELEMENT (OFHE/OFBE) for giving a haircut. The need to make simple, respectful, and reasonable assumptions became important, to enable teaching haircutting logically and correctly. Making the general assumptions that the human head was spherical and that the scalp/surface of origin was positively curved (which is not always or absolutely the case), I could simplify haircutting theories and consequently reduce the number of technical drawing and texts. Also, I saw the importance of proper formation of OFBEs in logical haircutting systems, when the division of one OFBE to form another can only be done with precision if all OFBEs are organized and cut precisely.
ORTHOCOURALOGY Patrick Patrick F. F. Garelle Garelle
At this level of research, I began to realize that teaching the art of haircutting could be done in a much easier and faster way. The study of what became the OFBE led me to write the theory of time for giving a haircut, and opened the door to quantification. Ultimately, the most important effect resulting from that analytical and rational approach was changing the way the art of haircutting could be taught. Opinion-based teaching theory could now be replaced by a far more efficient and simpler scientifically-based haircutting method. An ortho-prism (ortho-polyhedron) can be considered as having six faces. Its base is formally seen as spherical, therefore curved; the other faces are considered as being flat (not true such as when a face is formed from the hairline), and not all the faces have all straight edges.
Why did I name that temporary solid an ORTHO-PRISM? The ortho-prism I have defined in the program of orthocouralogy is, along with the ortho-pyramid, one of the basic elements of construction for giving a haircut logically in this methodology. When visually analyzed and dismantled, that element needed a name. The construction and purpose of this temporary formation of hair strands, as well as its use within systems and procedures, made me think that the ortho-prism had to have a name with a scientific value, not just to look good, but simply because it was needed to teach its values and uses. The ortho-prism had a geometric dimension and value, and the closest comparable structure was the triangular prism at first, then trapezoidal prism when more investigated, in solid geometry. Before calling this formation made of hair strands an ortho-prism, I had given it different names such as “segment-cut” (a term later applied to just the edge and apex of the orthoprism), “hair-prism” and “hair-pyramid.” Since the orthocouralogical methodology is a rational analysis of how to give a haircut logically rather than intuitively, I felt it necessary to use, name and define mathematically some important elements used to give haircuts, involving the manipulation of groups of hair strands. The reason I named this formation made of hair strands an ORTHO-PRISM is due to its resemblance to a triangular, then to a trapezoidal prism. However, with respect to traditional geometry, the ortho-prism is not considered as a prism since it does not have identical cross-sections when cut by a plane parallel to the base, which can’t be achieved since that base is spherical. Ortho-theoretically, making the assumption that the scalp is of spherical character, an ortho-prism could be seen as having two bases but would not be congruent or parallel. The base of an ortho-prism is considered to be spherical since it lies on the scalp.
ORTHOCOURALOGY Patrick Patrick F. F. Garelle Garelle
REMARK: That sixth face represents the apex of the OFHE, which in actual haircutting is also considered as the “actual (ortho) geometric segment-cut� or the true (ortho) geometric segment-cut in formal ortho-geometry when the holding fingers are not represented. That sixth face can be considered as the irregular face of the ortho-prism, since that face is made of hair strands end cross sections, which can be of irregular shape; and seen as a whole, that sixth face will most likely be squeezed irregularly and show irregular edges due to the irregular shape of fingers.
ORTHOCOURALOGY orthocouralogical tower
Image taken from the library of orthocouralogy
ORTHOCOURALOGY Patrick Patrick F. F. Garelle Garelle
Some important reasons to form small OFHEs Technical • • • • • • • • • • • • •
To get good visual reference segment-cut (Ref-SC) To keep a clear visual of the type/shape of reference segment cut To maximize the correct organization of all hair strands forming those OFHEs To cut more precisely and accurately The minimize the arc effect To have a precise, and accurate line of cut (LC) To avoid visual confusion The avoid losing the visual Ref-SC To minimize technical mistakes To minimize corrections To avoid choppy effects To avoid having to modify a desired technical haircutting action plan To avoid to have to change the desired artistic idea
Human factors (positive) • • • • •
Safer, more secure Increased sense of professionalism Increased sense of self-esteem Increased confidence of clients Reduced stress factors (both giver and receiver)
Physiological factors (positive) • • •
Less physical effort (relative to hair mass physical properties) More comfortable for the client Increased maneuvering speed
Choppy effect Poor formation quality of an OFBE can be responsible for a choppy effect. Poor formation of one or more OFBE has a direct effect on the physical properties of the LC. Poor technical sequencing of OFBEs and gaps (empty scalp) in hair growth on the surface of origin can also be responsible for a choppy effect. Obviously, differences in hair’s physical qualities are also a factor that can contribute to choppy effects. For example, an abrupt change of hair shape, such as from straight to curly, or an abrupt change of color (thick highlights on a layered surface area) can create that choppy effect, even when a haircut is given at the highest technical level.
ORTHOCOURALOGY Patrick F. Garelle
Ortho-Geometry Adaptation procedure applied to all OFHE/OFBE From an isosceles triangle to an ortho-isosceles triangle
Isosceles triangle
seen as a casual triangle since one edge is curved (base/scalp/ SO)
considered as 3 vertices
Ortho-Isosceles Triangle (adaptation for the domain of haircutting instruction)
O R T H O C O U R ✂ A L O G Y
3 vertices
3 vertices
actual geometric point/segment-/cut
true geometric point/segment-cut
An ortho-isosceles triangle might not have 2 equal angles on its base (due to SO irregularity)
Construction-Section
Surface of Origin/scalp (spherical)
2006
NEW YORK
SCIENCE AND ART
Orthocouralogy ORTHO-ISOSCELES TRIANGLE
5 Faces of an OFBE/Ortho-prism Smallest formation of an OFBE theoretical ONLY/not applicable OFBE: ORTHO-ISOSCELES TRIANGULAR PRISM
✂
O R T H O C Segment-Cut O ✂ U R 4 A 5 3 L O 1 G Y
- 5 faces - 6 vertices - 9 edges
2
1f
+ 2f
+ 2f
= 5f
ORTHOCOURALOGY Patrick Patrick F. F. Garelle Garelle
Ortho-geometry and Systems OFBE: ORTHO- ISOSCELES TRIANGLE PRISM
2 Ortho-quadrilateral control front & back wall faces Front wall face No. 2: The selected group of hairs about to be cut or being cut (shows being cut here)
O Back wall face No. 3: The selected R group of hairs previously cut. The back wall is the reference segmentT cut (Ref-SC) H✂ O 2 4 C 5 O U 1 R A L General ortho-symbol for OFBE/ortho-prism O G Y ORTHOCOURALOGY Patrick Patrick F. F. Garelle Garelle
3
ORTHO-ISOSCELES PRISM (OFBE most simple form)
2 Ortho-Triangular Ortho-prism Lateral Wall Faces
✂
3 4 5 ORTHOCOURALOGY 2
1
ORTHOCOURALOGY Patrick Patrick F. F. Garelle Garelle
ORTHO-ISOSCELES PRISM (most simple form)
✂
2
4
5
3
ORTHOCOURALOGY 1 1 ortho-spherical quadrilateral Base Face or Ortho-cell The ortho-cell is the OFBE base.
ORTHOCOURALOGY Patrick Patrick F. F. Garelle Garelle
The 6th Face of a Otho-Prism (the ghost Face) The Sixth Face of an Ortho-Prism (the “Ghost Face”) The sixth face is the least obvious to the eye. Due to its size and shape (quadrilateral, without complication), it changes the way the two lateral faces of an orthoprism are seen from a geometrical point of view. These two lateral faces, easily seen as ortho-triangles, become ortho-trapezoid/trapezoidal faces. For the purpose of simplification, the lateral faces are often represented as being ortho-triangular and the sixth face is represented by only a line segment, when it is no necessary to be so precise.
Location Less apparent because of its small size, the sixth face of an ortho-prism is located at the ridge apex of that structure/ortho-prism.
In actual haircutting That sixth face is the surface area created by the Actual Geometric Segment-Cut, which surface area is made of the hair strands’ end sections.
Remark about the “actual segment-cut” The actual segment-cut (SC) is generally located above the geometric SC, or just above the holding fingers. However, that SC can sometimes be below the holding fingers. What is important to know is that the actual SC, whether it is located below or above the holding fingers or above the longitudinal axis of the scissors, is always responsible for creating the sixth face, or the top face ridge of the ortho-prism. This means that the actual SC can be at the same time both the geometric SC and the actual SC.
Size of the sixth face The size of the sixth face’s surface area is relative to the number of single hair strands being selected to form an OFHE. The number of hairs, the diameter of each hair, and the size of the surface of origin/ortho-cell represent some of the factors that determine the size of the sixth face. Determining the size of the sixth face includes consideration of the hair’s physical properties as well as the level of operational precision. In terms of representation That sixth face is represented by the apex of the ortho-prism, which apex is a surface made of the hair strands’ end sections. That face, representing the True Geometric Segment-Cut, is often the one used as an example in technical figures.
ORTHOCOURALOGY Patrick Patrick F. F. Garelle Garelle
NO. 6 Faces of an OFHE/Ortho-prism
ortho-trapezoid trapezoidal lateral faces (4th and 5th face as indi-
✂ - 6 faces - 8 vertices - 12 edges
ORTHOCOURALOGY
✂
2 4 3 5 ORTHOCOURALOGY 1 interior hair are not represented
1f SPH + 2f
+ 2f
+
= 6f
ORTHOCOURALOGY Patrick F. Garelle
The NO.6 face is considered as being quadrilateral. Then, the lateral faces change to be ortho-trapezoid instead of triangular. - 6 faces - 8 vertices - 12 edges
The 6th face viewed form above
✂SC ✂
2
3 4 ORTHOCOURALOGY 55 1 4 5
Ortho-triangular faces become ortho-trapezoidal faces when the size of the ortho-prism increases from its minimum geometrical structural form to a more precise graphic conception.
ORTHOCOURALOGY Patrick F. Garelle
The plane B, which is a tangent plane of a spherical surface (OPH), is perpendicular to radius (CT) drawn to the tangency point T; a tangent plane of a spherical surface has only one common point with the surface – a tangency point. The Ortho-Geometric SC is a parallel tangent plane to the tangent plane B. Plan B is perpendicular to the radius CT, and plane SC perpendicular to the extended Radius CD.
Ortho-true geometric SC or plan/face N0. 6 SC not to scale
✂D
✂
lateral face (ortho-trapezoidal)
ortho-prism
T Plan B C
ORTHOCOURALOGY OPH
view from above (rotated 90 degrees)
✂ ORTHOCOURALOGY OFHE lateral faces
ORTHOCOURALOGY Patrick F. Garelle
Ortho-Fundamental Building Element Components of construction for giving a haircut
OFBE components of construction: The list of components that could to be part of the infrastructure of an OFBE.
Portion of Hair Line (HL) construction section CS transition section TS area boundary (AB) SC: PG REF SC, REF SC Part Altitude (all altitude edges) Surface of origin/ortho-cell dimensions and shape Shifting type
2006
NEW YORK
ART AND SCIENCE
Orthocouralogy SYSTEMS
OFHE/ortho-prism Formation Order
Stages of formation of an Ortho-Fundamental Building Elements
7 Stages Ortho-prism Faces: Formation Order Stages of formation of an Ortho-Fundamental Building Element (in brief) Stage 1: OFBE source of origin/ortho-cell framing (partial): size and shape of the OFBE base /ortho-cell. Stage 2: Partial development/formation: the physical formation of an OFBE Stage 2 includes new groups of hair and portions of the previous OFBE. This formation represents the main body of the OFBE. Stage 3: Setting the OFBE type to make it ready for cutting. This stage can be executed to form the PG Ref SC/initial REF SC, a Ref SC, or a change of OFBE type. Stage 4: The actual cutting action/making the segment-cut (SC). Stage 5: Decimation or release action: Ortho-decimation/Release: The OFBS is no longer held, therefore released from the holding forces. Stage 6: Verification procedure The line of cut (LC) is analyzed. Stage 7: Optional procedure If the verification analysis does not confirm satisfactory results, the OFBE will be reformed or restructured, and then cut or re-cut. Then...
ORTHOCOURALOGY Patrick F. Garelle
Formation order of an OFHE (simplified) 1: The OFBE base/ortho-cell 2: The front and back wall faces (commend shifting faces) 3: The lateral wall faces (define the type of OFHE) 4: then, the SC face (ridge/apex of the OFHE) Segment-Cut (SC) (Orthocouralogical Segment-Cut) There are two types of SCs. :1 The true geometric SC, which is represented by the ridge of the ortho-prism with out the representation of the holding fingers. The true geometric SC mostly considered as theoretical. 2: The actual geometric SC is were the cutting is actually performed whether it is below or above the holding fingers position.
ORTHOCOURALOGY O R T H O C O U R A L OG Y
ORTHOCOURALOGY Patrick F. Garelle
Examples of slanted OFHEs with a “square SC” (SC is at right angle with the shifting faces)
ORTHOCOURALOGY slanted OFHE/OFBE
ORTHOCOURALOGY slanted OFHE/OFBE
ORTHOCOURALOGY slanted OFHE/OFBE
ORTHOCOURALOGY Patrick Patrick F. F. Garelle Garelle
Ortho-geometry Two different descriptions In theory and based on the desired level of explanatory precision, an OFBE/ortho-prism can be seen as having 6points/vertices, 5 faces, and 9 edges. In actual haircutting, for higher explanatory level an OFBE/ortho-prism can be seen as having 8 points/ vertices, 6 faces, and 12 edges.
8 points, 6 faces and 12 edges of a typical OFHE
ORTHOCOURALOGY 6 points/vertices, 5 faces and 9 edges of a typical OFHE
2006 Š
NEW YORK
SCIENCE AND ART
Orthocouralogy Master Layering Systems
Functions of an OFBE (in brief) - To give a haircut - To verify a haircut - To specifically select groups of hair strands to be cut - To organize a selected group of hair strands - To control the direction of the selected group of hair strands - To better control the physical tension of selected group of hair strands - To prepare for the next OFBE to be cut (if indicated) - To reduce the volume of a hair mass in a specific way
Principle effects of an OFBE The physical effect of an OFBE after being released is relative to its geometrical shape, size, physical location, and the physical properties of the hair being treated. Each different OFBE has a proportional effect on the corresponding line of cut (LC).
ORTHOCOURALOGY Cannon PowerShot G7 7.4-44.4mm 1280 .960 November 6, 2006
Image taken from the library of orthocouralogy
ORTHOCOURALOGY Patrick Patrick F. F. Garelle Garelle
Orthocouralogy to match today’s technology, and behind The superficial need for humans to change their physical appearance, and their ingenuity in doing so, has given rise to the use and development of a large array of devices and technology. Man has left traces of tools designed to cut hair dating to before 2000 B.C. Millennia later, mostly during the 20th century, industrial advancements in manufacturing led to improvements in scissors, combs, and other hairstyling tools, along with the development of haircutting techniques. Taking advantage of all these, hairdressers are now equipped to give far superior technical performance beyond the art of haircutting. Researchers, engineers, and scientists are the leading agents of change in providing our industry with better performing tools. If one important focus is to improve the tools and technology of the trade, it is our opinion that currently, the contents and instruction of technical haircutting knowledge is now far from meeting the performance qualities of those tools. The point here is to lead our industry to understand that it is time for the quality of technical haircutting knowledge to rise to the very high degree of quality haircutting tools available on the market. It is my belief that because of the invention and development of orthocouralogy, it is now possible to participate at a greater level in the creation of better professional tools.
Introduction The research and study based on the assumption that haircutting could be learned, taught, and practiced logically began with the empirical observation and identification of what we have named the OFHE or OBFEs. The adaptation of mathematics to describe and define that temporary structure made of hair might well be considered the most important breakthrough in the creation and fulfillment of orthocouralogy. Without that invention, I believe orthocouralogy could truly not exist or become the potential educational tool it is today. It is my belief that without that mathematical adaptation, finding the key and opening the door to a new way of learning and practicing haircutting was impossible. As mentioned in JO-AD Issue No. 1, it is our belief that without the introduction of very elementary math to support simple, rational discourse, haircutting instruction could only stagnate and remain intuitively-based in its instruction. Selecting groups of hairs using hands and fingers as holding elements, and a comb as an organizing devise to cut a series of groups of hair, is proof of the human ingenuity behind the development and practice of haircutting. The invention of scissors and comb allowed humans to engineer different, more complex ways to give haircuts, using more sophisticated and precise systems. The beginning of the 20th century commenced the era of modern haircutting, when women began to cut their hair and haircut design started to become as important or more important than hairstyling alone. It became clear that talented stylists who cut hair were more progressive and eventually more successful than those who were giving Victorian-type hairdos.
ORTHOCOURALOGY Patrick Patrick F. F. Garelle Garelle
We must think outside the box in order to break through from traditional haircutting instruction. Making the reasonable assumption that the OFHE is the only technical element that can be used to give the greatest number of haircut designs at the greatest level of precision, we might reasonably understand that the OFHE should be independently analyzed in order to understand its technical values. This means that each type of OFHE (defined only in orthocouralogy) must be analyzed seriously in order to understand its importance when integrated into a mechanical haircutting system. Modification of how the art of hairstyling is taught has arrived with the creation of orthocouralogy. With the creation of orthocouralogy, teaching the art of hairstyling takes on a new dimension. Orthocouralogy replaces the very slow intuitively-based learning process with a much faster way of learning. It is also believed that by taking an analytical approach, the orthocouralogical program could very well attract new types of learners who comprehend by reading, analyzing, and listening, therefore opening the field to other than kinesthetic learning types. Without a rational explanation of how to give a specific haircut design, it is not possible to record, repeat, or transmit it. Repeating or approximating a previous haircut from memory may be possible; however, once forgotten, what may have been a great artistic success is lost. Nevertheless, the rational and correct explanation of a haircut given from an intuitive mindset is impossible. We all must understand that an assistant watching a hairdresser giving a haircut in an intuitive mode has been put an unfair situation, since this hairdresser is not able to explain what he/she is doing. Important statements and conclusions resulted from this study. These statements articulate some of the most important requisites of an instructor in orthocouralogy. • An instructor must have the best knowledge possible of what an OFBE is, and must explain it clearly to the student. • An instructor must emphasize the fact that correct formation and cutting of the OFBE is necessary in order to give a haircut at highest level of precision.
ORTHOCOURALOGY Patrick Patrick F. F. Garelle Garelle
Knowledge Test (Sample)
O R T 2: What term can be used to name the No. 1 face of an OFHE? • ortho-cell • shifting face H • ortho-face • OFBE O 3: Is the surface of the Chuman scalp (in reality) always positively curved? • yes • no 4: How many edges O does typical triangular OFBE/ortho triangular prism have? • 6 • 9 U • 7 • 12 R 5: How many vertices does a typical trapezoidal OFHE have? • 3 A • 6 • 8 L • 12 6: How do you verifyO if an OFHE is precisely formed? Circle the best answers. • By direct visual inspection • By verificationG of the line of cut (LC) 7: What are some possible outcomes of using large OFHEs? Circle the correct answers. Y . Choppy effects 1: What is another term for OFHE? • OFAHD • OFABHD • OFBE • ortho-group
. Loss of precise Reference segment-cut (Ref-SC) . Haircut finished quickly . Lower precision level . Less accuracy
Answers 1: OFBE, 2: ortho-cell, 3: no, 4: 9, 5: 8, 6: visual inspection, 7: all
ORTHOCOURALOGY Patrick F. Garelle