Dr. Dragone Issue #13

DR. DRAGON HSMSE’S MATH, SCIENCE, ENGINEERING AND ARCHITECTURE MAGAZINE

Stephen Hawking

“To confine our attention to terrestrial matters would be to limit the human spirit.”

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Dear Readers, Welcome to our Spring 2018 issue! Our little club started about six years ago. Since then, I am pleased to announce our continuing success as we approach our thirteenth magazine. We aim to constantly develop our knowledge in math, science, and engineering, and keep our readers interested in the STEM fields. Many thanks to all our staff members for continuously working hard for this magazine. Without them, this magazine would have been an impossible task. Much obliged to our faculty advisor, Mr. Choi, who supported us every step of the way. Special thanks to the HSMSE PTA for sponsoring this magazine.

Finally, I am grateful to our readers for reading this magazine. Enjoy!

Mia Akhter, President

STAFF PRESIDENT

DESIGNER IN CHIEF

VICE-PRESIDENT

EDITOR IN CHIEF

TREASURER

DESIGNERS

MIA AKHTER

AFSANA RAHMAN ANGELA JIANG

MAISY HOFFMAN

SECRETARY

NATHAN ELLIS ZELIE GOLDBERG LITTLE KOREEN GROSSBERG

FACULTY ADVISOR

SPECIAL THANKS

LISETTE PERES RONALD CHOI 2 1

FATEMA BEGUM

HSMSE PTA

WRITERS

MIA AKHTER KENYA CALDERON MAISY HOFFMAN MIN YI LIN FATOU MBAYE AFSANA RAHMAN ELVIRA QUARSHIE JASPER STEDMAN ROBERT TAYLOR

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THE Math OF MUSIC

MINING BITCOINS

SOLAR ENERGY

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ELEMENT 80 MERCURY

Ripples in time Stephen and space hawking MIA AKHTER

KENYA CALDERON

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Water on Mars

DR. VINOD MENON

HYPERBOLIC MATH

MAISY HOFFMAN

ELVIRA QUARSHIE

JASPER STEDMAN

MIN YI LIN

AFSANA RAHMAN

ROBERT TAYLOR

FATOU MBAYE

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The Mathematics of music Music is an art. It is a fabulous, beautiful force that brings people together and has evoked emotion and expression for millenia. In complete opposition, mathematics is a strictly logical and rational study.

These two subjects are seemingly oil and water; one is a form of wondrous, creative voicement, while the other is a study of pure reason. How are these subjects intertwined? In reality, they are not just related, the entire basis of music is mathematics. Math is applied to almost every aspect of music, whether deliberate or not.

First of all, what is music? Some might define music as any piece that utilizes melody and rhythm. While this covers most music, it excludes some parts of the rap genre, which occasionally forgoes melody altogether. This definition would also ostracize more avant-garde artists’ works, such as John Cage’s famous piece 4’33”, in which musicians come onstage to play nothing at all. There is no true definition of music, but 4’33” aside, music is sound. Now, what is sound? Sound is any vibration travelling through air that can be perceived by an auditory sense. These vibrations are waves with individual frequencies, which are measured in Hertz (Hz).

Each musical note has a set 11 frequency, which will remain constant from instrument to instrument.

In the crafting of musical instruments, artisans take extremely precise measurements in order to produce the correct sound. Musical tuners for instruments such as the piano train their ears for years in order to recognize standard pitch and the perfect sound that an instrument should produce. The concept of a mathematical measurement for a note’s tone had existed for a long time, before even Pythagoras lived.

It was also well known around his time that any given

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note shares the same sound one octave (eight notes) lower, if the Hz measurement is divided by two. Besides pure mathematics, Pythagoras and his exclusive math club had a deep interest in music. They, of course, applied their dedication to math to music as well. Either Pythagoras or a member of his group decided to experiment with the octave rule. He tested for the resulting sound when he divided a note’s Hz by three instead of two. Rather than another octave, the sound produced was a blissful harmony. When the resulting note was again divided by three, the sound created was another harmony.

This process, when repeated four times from the original note A, was called the Pentatonic Scale.

The Pentatonic Scale is used very commonly, as variations of the scale were developed independently in ancient times globally, in places such as China, Southeast Asia, and North America. There are further scales that use the same significant principle. The Chromatic Scale utilizes twelve notes, though some are dissonant with others. Musicians and music theorists, however, throughout thousands of years, have discovered all sorts of chords and sub-scales from these twelve tones.

Not only have musicians created so many chords and scales, but in every song is a set of chord progressions. A chord progression is a series of chords, and is the basis of both the melody and harmony of a song.

Certain chord progressions sound naturally “better” to us, because they utilize existing harmonies to connect chords and form hearty-sounding resolutions.

The most common chord progressions use this idea, as it automatically sounds nice to the ear. In fact, one of the most common chord progressions across all genres, known as I-V-vi-IV, is included in far over 500 songs.

These “normal” sounds, including chord progressions, influence an enormous amount of music.

Songwriters use chord progressions and series of notes that end in harmonic resolutions because they are incredibly familiar, so they sound immediately “good.” This immediate reaction is based in psychology. Throughout life, we are exposed to normalized chords and resolutions so much that we have an instantaneous mental pull towards one note after another in the context of music, because it will sound “natural” and gratifying. Most produced music today, especially with the help of technology, exploits these tonal tendencies to make music particularly catchy. Songs are sometimes specifically created in such a way that it is easily memorable because all the chords and sounds are expected mentally.

Mathematics in music occur naturally, but can be also manipulated to enhance certain parts of a song that might otherwise sound bland or dull.

By applying math to music, musicians impeccably infuse logic with art. However, despite all of the mathematical implications in music, purposeful or not, music is an art. Though math is wildly critical to music, it will never be able to explain the greatest moments of our favorite songs. The moments when the singer wavers on a note for just a split-second too long, or when the articulations of the bass line feel so emotionally matched to a song, or when the last strum of the guitar, while nearly out of tune, expresses a certain passion not included in the solid logic of math.

Music is ultimately a creative calling, only improved by math, and is thus such an important part of human history and culture.

Maisy Hoffman

Hart, Vi. “Twelve Tones.” Vi Hart, 7 June 2013, vihart. com/twelve/.

Jr., Jack H. David. “The Mathematics of Music.” The

Music, March 7 1995, jackhdavid.musicsensa tionsthehouseofdavi.com/papers/math. html.

“Mathematics and Music.” Mathematics and Music

Study | Simplifying Theory, www.simplifying theory.com/mathematics-and-music/.

“Sound | Definition of Sound in English by Oxford Dic

tionaries.” Oxford Dictionaries | English.

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Bitcoin Behind the Screens

Money and CryptoCurrency Money is an essential tool in everyday life which per-

mits exchange between goods and services. However, when a dollar bill is compared to a piece of paper, how does it differ besides being printed with George Washington’s face?

All money holds its value and power because people have faith in the currency and the government supporting it.

The general consensus and faith that money can be obtained through services of an individual in exchange of goods from others allows trade to function. Similar circumstances allow cryptocurrencies such as Bitcoin to gain value and popularity behind an anonymous and global network. Being independent of any bodies of government and providing an anonymous means of transaction, this virtual money threatens to replace physical paper money.

What does it mean to send a Bitcoin?

Bitcoin is different from money in that it is decentral-

ized, and it is not attached to a government or a state.

There is no one organization that manages Bitcoin’s production and location. Likewise, there is no one to investigate possible fraud.

it is instead shared within a decentralized peer to peer network between strangers, where any volunteer is able to 6 5

check for the legitimacy of bitcoin transactions.

Unlike videos and photos, which are easily shared and copied between networks simply by duplicating its representative data, bitcoin does not behave like a computer file but is instead an entry on a huge global ledger called the blockchain. If Alice wants to send Bob 5 bitcoins, she simply publicly announces the transaction, “Alice sent Bob 5 bitcoins.” This transaction is then entered as an entry on the ledger and is verified by any volunteer, called a miner, who upholds the blockchain system. Miners are rewarded for their work in bitcoins.

The blockchain records every bitcoin transaction that has ever happened, and as of late 2016, the complete ledger is about 107 GBs of data.

In essence, sending bitcoin is simply writing down a payment on a global ledger that everyone upholds and trusts. Because anyone can make a transaction or verify a transaction, the lack of trust between strangers against each other creates a mutual relationship between those who wish to use an anonymous digital currency and those who verify this transaction in payment of bitcoins that sustains the economy.

The Wallet and Key Because bitcoins do not exist in any physical form

and are not computer files that can be transferred nor copied, how exactly does a user keep track of bitcoins, spend them, or receive them? Bitcoin wallet software enables a user to use bitcoins through the use of a digital signature.

A digital signature proves the authenticity of a message through mathematical functions and prevents forging of a transaction.

This is done through utilizing a private key that creates a signature and a public key for others to check the legitimacy of the entry. This signature can be thought of as the intermediate stage that allows others to check that the user is the true owner of the public key address (where bitcoins are sent) without revealing the real private key. A signature is generated with the private key and a transaction through what is known as a one-way function.

These functions state that is it easy to generate an output with a given input.

However, the reverse is so extremely secretive and difficult that it is only solvable through sheer guessing. Miners, those who guess and verify transactions with the rightful owner, update the ledger and continue the blockchain in reward of bitcoins to themselves. Because unique signatures are generated with each transaction, this also prevents the same transaction to be copied and forged by other strangers on the network. The wallet, however, unlike its suggested name, does not keep track of account balances but instead downloads and links to previous transactions to determine the flow of bitcoin deposits and its users.

Future of the Currency While the public attitude towards cryptocurrency re-

mains skeptical, it may be only a matter of time before people adapt to terms with the new technology as a more convenient way of life. Some economic giants such as China have already embraced the use of digital currency through software such as WeChat and Alipay to pay for services such as rent, groceries, taxi and street food! As the use of cellular devices and electrical communication becomes more prominent, paper money may no longer be a necessity for modern living.

Min Yi Lin Driscoll, Scott. “ImponderableThings (Scott Driscoll’s

Blog).” How Bitcoin Works Under the Covers,

1 Jan 5. 1970, “Everything You Need to Know Bitcoin Mining.” www.bitcoinmining.com/.

“What Is Bitcoin?” CoinDesk, 29 Jan. 2018, www.coin desk.com/information/what-is-bitcoin/.

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SOLAR POWERED FLIGHT

The around-the-world flight of the Swiss Solar Impulse II, from March 2015 to July 2016, was an energy milestone.

The plane flew 40,000 km (25,000 mi) completely on solar power and proved that it can be used for sustained flight.

The goal was to pilot a solar powered airplane on a circumnavigation of the earth in twenty to twenty-five days and to draw attention to clean energy options.

Due to weather and technical problems, the flight actually took sixteen months instead of 25 days, even though actual flight time was 23 days. New technologies take a very long time to become efficient and reliable enough to be adapted for everyday use. Consider that the very first working steam engine was invented in 1606 by Spanish mining engineer, Jerónimo de Ayanz, to pump water out of flooded silver mines, and the first working railway steam engine was developed in 1804 by Englishman, Richard Trevithick. These steam engines, or external combustion engines, would lead to internal combustion engines, and later gas turbines and nuclear reactors. Wood fueled the first engines; later engines were fueled by coal, oil, gasoline, diesel, and now nuclear fuel because of its greater power density. Sailing ships and horse-drawn wagons were replaced by steamships and railroads, and now trucks and planes, all due to the greater power density of their fuel. If we

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have come this far since 1606, four hundred and twelve years ago, imagine what solar power will look like in the year 2430!

What “solar power” really means is how much energy a battery can hold when it is charged by collecting light from the sun. The light collected is then concentrated, turned into an electrical current, and then stored. How much energy a battery can hold is the most critical component of solar power usage.

Solar cells make up the skin on all solar powered aircrafts. The most effective form of solar cells are photovoltaic, meaning that they convert sunlight into voltage and electric current via the semiconductor materials in the panels. The first photovoltaic module was built by Bell Laboratories in 1954 and they work by converting light at the atomic level into electricity.

This was very expensive to produce at first and there was little interest in it until the space industry needed a source of power aboard spacecraft. As the space industry advanced, photovoltaics advanced as well, and ultimately became more reliable and cheaper to produce. Solar cells are made of silicon similar to semiconductors. For solar cells, a thin semiconductor wafer is treated to form a positive and negative field on either side. When light energy hits the solar cell, electrons are released from the atoms, and an electrical current is generated and can be used as power. Solar cells electrically connected to each other and mounted together are called a photovoltaic module. Multiple modules connected together form an array, and the larger the area of an array, the more electricity is produced. Silicon-wafer cells have light absorbing layers that are traditionally 350 microns thick, but new thin-film solar cells have light absorbing layers that are just one micron thick (i.e. 1/1,000,000 m, 1 Âľm, one millionth of a meter) and absorb energy from the sun efficiently and are durable and easy to use.

Energy storage represents the primary inefficiency of a solar powered plane because the weight of a battery is heavier per square meter than the weight of gasoline per square meter. With thousands of solar panels charging the four lithium-ion batteries that power the four motors on the Solar Impulse II, the plane can fly at night from stored energy in the batteries. Every morning the plane climbs to 8,500 meters to capture the most sunlight, and the gradual descent to 1,000 meters at night is in itself energy saving. The plane can go as fast as 100 miles per hour but is most efficient at 60 mph. Each bat-

tery contains 70 lithium-polymer cells, and similar batteries are used by virtually all drones, re-entry vehicles, and electric planes. The surface area of Solar Impulse II is 269.5 m2 and has 17,248 photovoltaic solar cells that cover the wings, fuselage, and tail. The Solar Impulse II has a wider wingspan than a Boeing 747. It can stay aloft for one full cycle of day and night but must be recharged during that cycle.

To determine the output of a solar power energy system for an aircraft, it is important to understand what forces are trying to bring the aircraft down, and then to understand what forces are needed to keep the aircraft up.

MIT offers a course called “Flight Thrust, Power, and Energy Relations� to understand those forces.

The Li-ion batteries on the Solar Impulse II were produced by Air Energy of Germany and have an energy density of 260 Wh/kg. Each battery weighs 633 kg, or 1,395 pounds, the weight of a small car!

Difficulties for Li-ion batteries include temperature extremes, oxidation, weight, and lifespan. Monoflourethylencorbonat solvent is added to the lithium-ion batteries during testing, and depending on the blend it can result in higher energy density. To help with tempera-

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ture fluctuations, the areas around the batteries are heated and new insulating foam developed by Bayer Material Science covers the batteries. Batteries are kept independent of each other, and a balancing controller ensures even power between cells. Particular solar panels feed each battery, and each battery powers a specific motor. In case a motor fails, the solar feed and power from other battery can be switched to the remaining engines. The margins for error and safety are narrow, but batteries are the critical component to keep a solar aircraft in the sky. As energy density rises, these margins will widen and make solar powered planes more accessible.

Solar powered flight requires a lightweight, efficient, and reliable engine. Weight is the critical concern because greater weight results in greater power needs.

Several different electric motor designs have been developed over the years and the three best options are The AC induction motor, the DC motor with brushes and permanent magnets, and the brushless DC motor with permanent magnets. Because AC Induction motors have high Joule losses in the rotor, and DC motors with brushes and permanent magnets have power losses due to the inefficiency and extra weight of the brushes, the brushless DC motor with permanent magnets is the

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best option. To optimize performance, the brushless motors are fitted with reduction gear that limits the rotation speed of the propellers to a slow and consistent revolution. The output of the motors is 6 kW andabout 8 horsepower during a full cycle of night and day, which is equivalent to the same amount of power in the Wright brothers’ plane.

The single most critical component of solar energy is battery power density.

With advancements in solar technology and in the chemical compositions in batteries, there will soon be breakthroughs is battery power density. When batteries can store more power, kilowatt hour cost will decline significantly and solar powered batteries will begin to supplement fossil fueled engine needs. When the hurdles of weight, size, reliability, and efficiency are overcome, solar-powered engines can replace fossil fueled engines which will dramatically cut carbon emissions and make travel less expensive.

Robert Taylor NASA. “Solar Airplanes .” NASA, NASA, www.grc.nasa. gov/WWW/K-12/airplane/inleth.html.

NASA. “Solar Cells - NASA.” NASA, NASA, science.nasa. gov/science-news/science-at-nasa/2002/solar cells/.

“Solar Powered Drones, Coming Soon To A Sky Near

You.” CleanTechnica, 10 May 2016, cleantechni ca.com/2016/04/29/solar-powered=drones.

Mercury Atomic Number 80 What is Mercury?

Mercury is a chemical element with the symbol Hg and

atomic number 80. It is the only metal that is a liquid at Standard Temperature and Pressure (STP). It is commonly known as quicksilver and formerly known as hydrargyrum. Its density is 13.6 g/cm3 at STP. The melting point of mercury is -38.9 °C, and its boiling point is 356.6 °C. Despite being a metal, mercury is a poor conductor of heat, but it still conducts electricity. It alloys easily with other metals like gold, silver, and tin. Mercury has a high density and a consistently high rate of thermal expansion over a wide temperature range, so one of its main applications is in thermometers. Metallic mercury is usually not harmful when it is trapped in household items like lightbulbs, but when a thermometer breaks, a significantly dangerous exposure to mercury may occur through breathing for a short period of time while it vaporizes. Exposure to mercury can be severely damaging, resulting in maladies such as nerve, brain and kidney damage. Mercury can also cause DNA damage, disruption of the nervous system, allergic reactions like rashes, and negative reproductive effects like miscarriages in humans.

fast and close to the nucleus. Understanding unusual aspects of science, such as the chemical anomaly of mercury, is incredibly important to the future of scientific research. Without an understanding of exceptions in science, we would never be able to go so in-depth with our knowledge of the world.

Elvira Quarshie Helmenstine, Anne Marie. “Why Mercury Is a Liquid at

Room Temperature.” ThoughtCo. N.p.,

n.d. Web. 22 Mar. 2018.

“Mercury - Hg.” N.p., n.d. Web. Martin, Gary. “’As Mad as a Hatter’.” Phrasefinder.

N.p., n.d. Web. 18 Mar. 2018.

“As Mad As A Hatter” The phrase “as mad as a hatter” is used lightheartedly

to describe someone as crazy. Many people associated this term with the Mad Hatter, a character in Lewis Carroll’s book Alice in Wonderland. The origin of this phrase stems from the 19th century, when mercury was used to make hats. The exposure to mercury made hat makers, or hatters, tremble and appear insane. Mercury poisoning is still known today as “Mad Hatter’s disease.”

Why is Mercury a Liquid?

Mercury is not like other metals in the periodic table.

Many metals are solid and great conductors of electricity due to their free-flowing valence electrons. They freely share their electrons with other atoms. Mercury is the exception. Mercury is a liquid at STP. This is due to the fact that mercury’s valence electrons are more tightly wound than usual to the nucleus. Its electrons move

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Ripples in Time and space Recognized with the 2017 Nobel Prize for Physics, Albert Einstein’s theory of general relativity has been proven correct. In 1915, Einstein determined that gravity is caused by changes in the geometry of space and time. Massive objects cause a distortion in spacetime, which is felt as gravity. Spacetime is any mathematical model that fuses the three dimensions of space and the one dimension of time into a four dimensional continuum. The larger the object, the more spacetime is distorted by that object. Any mathematical object that combines space and time, such as a black hole, would create ripples that move across the universe at the speed of light. Gravitational waves are the ripples in the curvature of spacetime that travel outward from the source of the distortion, like pebbles thrown in a pond.

What are Gravitational Waves?

Scientists suggest that gravitational waves are cre-

ated when two highly dense objects, like two black holes or two neutron stars, orbit one another. The interaction between these objects coil time and space, creating ripples. Detecting and analyzing the information carried by gravitational waves will allow us to observe the universe in a way never before possible.

It can open up a new window of study on the universe, give us a deeper understanding of these catastrophic events, and guide us towards cutting-edge discoveries in physics, astronomy, and astrophysics.

Looking closely at the cosmic microwave background, we gain an image of the universe about 380,000 years after its beginning.

There are patterns that can be found in the structure of the universe, such as galaxies and clusters. These patterns were caused by very tiny, random perturba-

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tions from the time when the universe expanded rapidly, known as inflation.

Though gravitational waves were predicted to exist in 1916, actual proof of their existence did not arrive until 1974, 20 years after Einstein’s death.

Though gravitational waves were predicted to exist in 1916, actual proof of their existence did not arrive until 1974, 20 years after Einstein’s death.

That year, two astronomers working at the Arecibo Radio Observatory in Puerto Rico discovered a binary pulsar—two extremely dense and heavy stars in orbit around each other. This was exactly the type of system that, according to general relativity, should radiate gravitational waves. Knowing that this discovery could be used to test Einstein’s audacious prediction, many astronomers began measuring how the period of the stars’ orbits changed over time. After eight years of observations, it was determined that the stars were getting closer to each other at precisely the rate predicted by general relativity. This system has now been monitored for over 40 years and the observed changes in the orbit agree so well with general relativity, there is no doubt that it is emitting gravitational waves.

The First Detection FInally, in 2016, the advanced LIGO (Laser Interfer-

ometer Gravitational-Wave Observatory) announced the first ever direct detection of gravitational waves.

LIGO, located in Livingston, Louisiana and Hanford, California, is a large-scale physics experiment and observatory to detect cosmic gravitational waves and to develop gravitational-wave observations as an astronomical tool. Reaching 4,000 meters, it is the seventh longest building in the world. A pair of black

holes, weighing in at 29 and 36 times the mass of the sun, merged into a single object, producing the ripples in space-time that LIGO detected.

The signal in September, 2015 was the first detection of binary black holes. Physicists Kip Thorne and Barry Barish of the California Institute of Technology, and Rainer Weiss of the Massachusetts Institute of Technology, received the 2017 Nobel Prize in Physics for their roles in the discovery.

The LIGO team announced its detection of a second gravitational wave signal in June 2016.

The observatory announced a third detection in June 2017 and a fourth detection in September 2017. The first four gravitational wave signals detected by LIGO were all created by pairs of colliding black holes. The fourth detection was significant because it was also detected by the Virgo gravitational wave detector in Italy. Virgo is a collaboration between the National Center for Scientific Research (CNRS) in France and Italy’s National Institute for Nuclear Physics (INFN). As LIGO and Virgo continue to study space-time, and as more detectors come online, such as one proposed

by India, scientists will improve their understanding of intermediate black holes and black hole pairs.

Types of Gravitational Waves The universe is filled with incredibly massive objects that undergo rapid accelerations. LIGO has therefore created different categories for different types of gravitational waves. These categories, Continuous Gravitational Waves, Compact Binary Inspiral Gravitational Waves, and Stochastic Gravitational Waves, are each unique. Continuous Gravitational Waves are produced by a single, spinning, massive, and extremely dense object, like a neutron star. Any bumps or imperfections in the spherical shape of this star will emit gravitational waves.

Compact Binary Inspiral Gravitational Waves are produced by orbiting pairs of massive and dense objects

like black holes, dwarf stars, and neutron stars.

Compact Binary Inspiral Gravitational Waves are produced by orbiting pairs of massive and dense objects like black holes, dwarf stars, and neutron stars.

These compact objects revolve around each other and send off gravitational waves, which removes some of the energy that keeps them from colliding.

Additionally, many small gravitational waves pass by from all over the universe all the time, and they are mixed together at random. These are called Stochastic Gravitational Waves. These are the smallest and most difficult waves to detect, but it is possible that at least part of this signal may originate from the Big Bang, which may allow scientists to see farther back into the universe than ever before.

Luckily for us here on Earth, though the origins of gravitational waves can be extremely violent, by the time the waves reach the Earth, they are millions of times smaller and less disruptive.

In fact, by the time gravitational waves from the first detection reached LIGO, the amount of spacetime wobbling they generated was thousands of times smaller than the nucleus of an atom! Such inconceivably small measurements are what LIGO was designed to make. The study of gravitational waves may one day reveal to us what exactly occured during and right after the Big Bang, and analyze the universe in a way never before possible.

Mia Akhter Cofield, Calla. “Gravitational Waves: Ripples in Space time.www.space.com/html.

“What Are Gravitational Waves?” LIGO Lab Caltech, www.ligo.caltech.edu/page/what-are-gw.

“What Is a Gravitational Wave?” Physics.org, www. physics.org/article-questions.asp?id=138.

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Stephen Hawking Stephen William Hawking was born on January 8, 1942, in Oxford, England. He had three siblings: two younger sisters and an adopted brother. His father was a wellknown researcher in medicine, and his mother was a political activist. As a child, Hawking exhibited great talent and was considered to be a child prodigy. At the age of eleven, he attended Oxford University, like both his parents had. His father urged for him to focus on medicine, but he elected to study physics instead. There, he further showed his talent and intelligence. His physics tutor, Robert Berman, described Stephen Hawking as an “extraordinary” student. He was able to solve theorems and solutions in a way that other students could not, utilized few books, and did not take any notes in class.

In 1962, Oxford university awarded him a first class honors degree in natural science.

Hawking went on to attend Trinity College in Cambridge to research cosmology and theoretical astronomy. During his first year, he started to show symptoms of neuromuscular problems, as he would suddenly trip and fall, and his speech slurred. At the young age of 21, Hawking was diagnosed with the life-threatening Lou Gehrig’s disease, or Amyotrophic Lateral Sclerosis (ALS). ALS is defined as a progressive degeneration of the motor neurons of the central nervous system, leading to a decline of the muscles, and eventual paralysis.

He was given a lifespan of two years. Hawking began to concentrate fully on his research, and even earned a PhD in cosmology. In 1965, he married a language student named Jane Wilde.

Stephen Hawking achieved many things that few could achieve in their lifetime.

In 1970, he developed a mathematical model for Albert Einstein’s General Theory of Relativity, and showed that the theory suggests space and time beginning when the universe was born, and ending within black holes.

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Hawking focused more on black holes, and in 1974, the “Hawking radiation” theory came to place. His theory states that black holes leak energy, before eventually evaporating and disappearing. Hawking also predicted that following the creation of the universe, or the Big Bang, black holes as tiny as protons were created and were governed by gravity and quantum mechanics. His groundbreaking work and discoveries did not go without notice, as he received numerous awards, such as the ‘Albert Einstein Medal’ and an honorary doctorate from the University of Oxford.

Hawking gradually lost control over his speech, and it became very difficult to understand him.

Unfortunately, in 1985 he lost his voice altogether after an emergency tracheotomy. An electronic voice synthesiser was created for his condition, which allowed him to select words through moving the muscles on his face and head.

In 1988, Hawking published a book entitled “A Brief History of Time”, a simplified explanation of physics for the public.

The book was an instant bestseller, and it gave him worldwide prominence. He continued to write and publish his works, which included an abundance of essays.

He also contributed to a book on Euclidean quantum gravity. Hawking also appeared on television in numerous documentaries, and became a very popular figure in science.

Stephen Hawking and Jane Wilde had three children together: Robert, Lucy, and Timothy. He later had three grandchildren. Hawking and Wilde had a divorce in 1995, due to strains on their marriage. Hawking’s health decline and increasing global popularity became too much for Wilde, so they decided to part ways. He married one of his in-home nurses, Elaine Manson, in Sep-

tember of that same year. His new marriage had a negative impact on his family, as they felt excluded from his life. They even worried about Manson physically abusing Stephen, but he publically denied such claims.

Police investigations took place, but were subsequently closed due to Hawking refusing to make a complaint.

The couple divorced in 2006.

By 2009, Hawking lost control of his hand.

He could no longer independently drive his wheelchair.

Since then, he was in and out of the hospital frequently, and experienced breathing difficulties. At times, he needed a ventilator. His health deteriorated overall. Stephen Hawking passed away at the age of 76 on March 14, 2018, at his home in Cambridge, England.

Stephen Hawking will be remembered for his major contributions to science, including his research on black holes and the existence of the universe.

”Try to make sense of what you see, and wonder about what makes the universe exist. Be curious.”

- Stephen Hawking

He received a plethora of awards and honors, and even has a movie reviewing his life called The Theory of Everything (2014). Hawking will forever be remembered for living a very long, fulfilling life after his diagnosis with ALS. The world is thankful that he lived for more than five decades after he was projected to only live two more years.

Kenya Calderon “About Stephen.” Stephen Hawking, www.hawking. orguk/about-stephen.html.

Editors, TheFamousPeople.com. “Who Is Stephen

Hawking? Everything You Need to Know.”Facts,

Childhood, Family Life, Research, Achieve

ments & Timeline, 18 Mar. 2018.

Pettinger, Tejvan. “Stephen Hawking Biography | .” Bi

ography Online, 15 Jan. 2018, www.biography online.net/scientists/stephen-hawking,dart mouth.html.

“Stephen Hawking.” Biography.com, A&E Networks

Television, 22 Mar. 2018, www.biography.com/ people/stephen-hawking-9331710.

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Where’s the Water on Mars?

The Red Planet has fascinated people for as long as we have watched the sky. It was specifically noted on Egyptian star maps over 3,500 years old. However, it was only in the late 1600s that astronomers began to realize that Mars was an entire world, not just a pinpoint of light.

Captivated by its vast, mysterious landscapes and features, they immediately compared it to Earth, making claims about its climate and the people and animals living on it. In 1781, astronomer William Herschel said that “Mars has a considerable but moderate atmosphere so that its inhabitants probably enjoy a situation in many respects similar to ours.”

All these centuries later, we know that Mars is almost nothing like Earth, but we are still searching for similarities.

li, made a map of Mars that included what he called “canali,” simply meaning “channels.” He soon realized that the lines were an illusion caused by his telescope, but his maps were already released in America, where “canali” had been mistranslated to “canals.” This caused excitement across the country, with many noted scientists claiming to also see global, man-made canals on the surface. Although the mistake was eventually spotted, and evidence quickly piled up that Mars was actually a barren desert, public interest did not waver.

Sensational science fiction stories continued to speculate about the Red Planet, offering theories ranging from ancient, advanced civilizations using canals for irrigation as their planet withered away, to the canals being used for transport through dense jungles with red leaves instead of green.

Most importantly, we search for the presence of liquid water.

Modern science has revealed much about Mars in the last 75 years.

If humans ever begin to colonize the Red Planet, having a source of water will be key to survival. Water is needed for life to function, but it can also be used for growing crops, radiation shielding, and can be broken down into oxygen and hydrogen rocket fuel for a return trip.

In 1965, Mariner 4 flew past and captured the first close up images of the surface, depicting vast, empty deserts.

Despite apparent desolation, scientists have continued to search for signs of water that could harbor microbial life. While there are definitely no canals, the scientific consensus is that there used to be water covering much of the surface. The smooth shapes of many landforms, along with mineral deposits, suggest that there was

The idea of water flowing on Mars dates back to the 1890s, when Italian astronomer, Giovanni Schiaparel-

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once flowing water. The Curiosity Rover has found ancient river beds, and satellites have determined that such river beds flowed into and out of ancient lakes. Additionally, there is likely ice underneath the south pole, covered in frozen carbon dioxide.

If there was so much water billions of years ago, where is it now?

Liquid water cannot exist on Mars today because its atmosphere is so thin that water evaporates instantly, and it is so cold that any water that does not evaporate freezes. For oceans to have existed, the air would have had to be much thicker, and the surface much warmer about 3.8 billion years ago, so the signs of ancient water tell a lot about Mars’ past. Mars is currently considered geologically dead, meaning there is no sign of volcanic eruptions or shifting tectonic plates. If volcanic eruptions were common in the past, then the gases released may have thickened the atmosphere and warmed the planet, and when the geological activity stopped, the atmosphere would have been blown away into space by solar wind, the constant stream of high energy particles from the sun. Earth’s atmosphere is safe from solar wind because it has a magnetic field shielding it from most radiation, but Mars has almost no magnetic field.

While most of the water evaporated, some of it also froze.

Satellites have used radars to find very dense ice buried beneath the Martian dust, much like the permafrost in the Arctic. Some water may have even seeped into surrounding rocks. A 2017 study in the journal Nature

concluded that because Mars rocks are very porous, up to 9% of the surface rock could be filled with water.

The search for liquid water still persists today. Between 2011 and 2015, scientists observed what appeared to be liquid water running down the dunes. Using the High Resolution Imaging Science Experiment (HiRISE), dark streaks were found on the side of some dunes, which trickled down in the summer and then disappeared in the winter. This result was the first evidence that water was still flowing on Mars, albeit in small amounts. While the results are very promising, a more recent analysis has shown that the dark streaks could also just be darker dust being blown over by summer winds. Unfortunately, this seems far more likely, though not nearly as exciting.

Perhaps the important reason for finding liquid water is that it is crucial for the emergence of life. If microbial life emerged back when Mars was warmer, then any liquid water on the surface today could be its last refuge. The discovery of extraterrestrial life, even the last survivors of a once flourishing species, would completely revolutionize biology and our understanding of the universe.

Jasper Stedman Dundas, Colin M., et al. “Granular Flows at Recurring

Slope Lineae on Mars Indicate a Limited Role

for Liquid Water.” Nature News, Nature Publish

ing Group, 20 Nov. 2017, Greicius, Tony. “Steep Slopes on Mars Reveal Structure

of Buried Ice.” NASA, NASA, 11 Jan. 2018, www. nasa.gov/feature/jpl/steep-slopes-on-mars-re veal-structure-of-buried-ice.

Hotakainen, Markus. Mars From Myth and Mystery to

Recent Discoveries. Springer US, 2009.

Redd, Nola Taylor. “Water on Mars: Exploration & Evi

dence.” Space.com, www.space.com/17048 water-on-mars.html.

Scishowspace. “Maybe There Isn’t Liquid Water on

Mars.” YouTube, YouTube, 24 Nov. 2017.

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Interview - Dr. Menon Dr. Vinod Menon is a professor of physics at the City College of New York and Graduate Center of CUNY. He grew up in India and earned his M.Sc. in Physics (Quantum Optics) in the University of Hyderabad, and his Ph.D. in Physics at the University of Massachusetts. His research involves the exploration of light-matter interaction at the nano-scale.

in photonics research. One of the most rewarding aspects of my job is student training in research. I have about 12 students working in my lab on various projects and they range from post-doctoral researchers, PHd students, undergraduates and high school students. Teaching is integral in my job and it helps me interact every semester with a new set of young minds and keeps my work fun. I love doing what I’m doing. I think academia is one of the few places which allows you the freedom to do what you love without too many questions.

Can you briefly explain what your research is about?

We want to understand how light interacts with mat-

ter on a nanoscale. At that length scale, you can make light do things it can’t normally do because light travels so fast through materials, it does not interact with them so much. Our goal is to slow down light, essentially trapping it, so that it interacts with materials much longer.

Tell us a bit about yourself, and how you got started working in nanotechnology.

My desire for science started in middle school. It

wasn’t clear what science I wanted to go into, but I was initially interested in robotics and artificial intelligence. I read many popular science books on topics about physics and string theory, but optics caught my attention. Later on, I wanted to work on theory.

When I got my Master’s, I gathered some experience about how it was to work in a lab.

I wanted to do optics experiment as my PHd, and for my post doctorate, I was at Princeton University working with optics and nanoscale materials, specifically the interaction between them. In 2005, I became a professor at CUNY, to build on their existing strength

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One example where our research might have applications is with solar cells. Sunlight gets absorbed by the cell and is converted into electricity. If you want to increase the number of photons (light particles) absorbed, you need to make the solar cell thicker.

But when you make the cell thicker, you can increase its absorbance, but it also increases the distance the electron have to travel before being detected thus affecting the overall efficiency of the cell. Thus, you would want to make the cell thinner. But then the other issue arises where enough photons can’t get absorbed.

What’s the solution? A simple way to increase the absorption of photons while maintaining a thin structure, is to take the thin layer and put it on top of a mirror or in between two mirrors. When light reaches the cell, what doesn’t get absorbed is reflected back to the cell by the mirror. You can create a system with these mirrors where light gets trapped so many times, it slows down, effectively increasing the efficiency of the solar cell. These are mirrors made of nanoscale thick materials.

We are also working with half-light half-matter quasiparticles that have qualities of both light and mat-

ter. These quasiparticles are realized due to strong interaction between light and the nanomaterials and they are called quasiparticles because they are not real particles and only emerge under this strong interaction with light. One of the biggest advantages of light is that it travels fast and goes long distances. However, a drawback of light is that it doesn’t interact with itself. One needs interactions to create devices such as switches that go between on and off state and transistors that can be used for logic operations. So how do we control the light? By adding a material component, we create these quasiparticles that are like half light and half matter.

The matter component is essential to the quasiparticles to create interactions. Thus, the quasiparticles, though it does not travel at the speed of light due to its material component, travels at a great fraction of that, and its material part allows it to have interactions, getting the best of both worlds.

few photons from the fiber, and build up the information you’re communicating. Hence, we use encryption which relies mathematically difficult problems that take long computational times such as factoring large prime numbers. It was theorised in the 90s that using a quantum version of a computer, one can factorize large prime numbers in a reasonable time by using the fact that multiple states can be simultaneously evaluated.

What do you hope to achieve with your research?

Our research is going in three directions:

3. Lastly, we want to do chemistry with light. Can we take molecules, and change their chemical states?

We’re putting molecules in between mirrors, and because of their interactions with light, we are trying to modify the energy levels of molecules, resulting in a unexpected changes to the molecular properties such as suppression of reactions.

1. We’re trying to see if these quasiparticles can be used in the emerging field of quantum technology.

Quantum mechanics is a field where you can have superposition of particles. To explain what superposition is, let us look at the example of Schrödinger’s cat, where it can be alive and dead simultaneously.

You have a cat with a vial of poison inside a black box. If the cat taps the vial, the poison might come out, killing it, but if the cat doesn’t tap the vial, the cat is alive. If you don’t look into the black box, you can’t tell whether the cat is alive or dead. Thus, we have to conclude that the cat is both alive and dead, since we cannot assume what state it is in, which is how quantum superposition works. In simple terms, Schrödinger stated that if you place a cat and something that could kill the cat (a radioactive atom) in a box and sealed it, you would not know if the cat was dead or alive until you opened the box, so that until the box was opened, the cat was (in a sense) both “dead and alive”. In our case we are interested in understanding the quantum properties of these quasiparticles.

2. We are also looking into how our work can benefit with securing communication, using the quantum properties of light. Suppose you and me are communicating using classical channels, or fiber optics, where light carries the information, through ones and zeroes. Someone can hack into this line, get a

IBM, Intel, Google, Microsoft, are all seeing the future of quantum computing. We are not building quantum computers - but instead trying to build small building blocks towards this larger enterprise of quantum computing such as a carrier of quantum information the single photon. So when you send information via single photons (a quantum particle) instead of classical channels, then immediately you will know when somebody has eavesdropped.

Can you give some advice to high schoolers who are interested in pursuing science or thinking about doing research in the future?

You need to be motivated and passionate about your interests. Being motivated, being driven, and working hard is essential to succeed. Also, get your fundamental concepts down. This is a nice phase in your life, from highschool to undergraduate, where you have time to solidify your concepts. Once you have the basic concepts down, you can get into fields and think about solving problems. Try to find connections between fields, like for example between neuroscience and optics. Get a broad experience in the beginning of your career, but go deeper into topics when you get into grad school. Find ways around problems.

Networking and collaboration are also important.

But remember, no matter what challenges you face, keep your motivation high.

Afsana Rahman

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HyperBolic Math

Straight lines look straight, right? That is probably what you have learned in geometry class. However, that is wrong‌ according to non-Euclidian math. Euclidean math is the form of geometry that almost all schools teach, but it is not the only type. There are other types of geometry that are not Euclidean. One of the most intriguing is hyperbolic math.

What is Euclidean Math?

Euclidean math is geometry that agrees with all of the 5 postu-

lates created around 350 BCE by the Alexandrian mathematician Euclid. First, we must define a few key geometry terms. A postulate is something we hold to be self-evidently true without having an exact proof of it. An axiom is very similar to a postulate, the difference being that axioms are not limited to only geometry. A theory however, we have to prove true.

The 5 Postulates Euclid detailed his postulates as follows: first, given any two

points, you can draw a straight line connecting both. Likewise, given any two points, you can draw a straight line segment containing both. Second, any segment you have constructed from two points can be extended indefinitely to form a line.

Third, with any given line segment, you can always draw a circle, using one point as the center, one as a point on the circumference, and the length as the radius. Fourth, all right angles are congruent to one another. The fifth postulate, however, states that if there are two lines cut by a third line, and the sum of the the two interior angles is less than 180, then the first two lines will have to converge at one point when extended indefinitely. This can be extrapolated to mean that parallel lines on a singular plane will never cross, but any other lines will.

Non-Euclidean Math Other mathematicians mostly agreed with these postulates.

They believed that the fifth postulate, rather than being a postulate, should be a theorem. Think of it this way; if the sum of the first two interior angles is 179.9999999999, you would have to extend the lines out very long before they converge, if ever.

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We have no way to actually prove that the two lines will touch if extended out so far, so we cannot hold it to be self-evidently true. However, if it were a theorem, then we could try to prove it using the other four postulates. One way is by using an indirect proof, trying to contradict this idea. That is where another postulate comes into play, logically equivalent to Euclid’s fifth postulate.

This is called Playfair’s axiom, and it states that given a line, l, and a point not on that line, p, there is only one line parallel to the line l, containing point p. To negate or contradict this introduced the two types of non-Euclidean math. One negation says that there are no lines that are parallel to line l that contain point p, resulting in elliptic geometry, or spherical geometry. The other negation states that there are infinitely many lines that pass through point p, and are parallel to line l. This is called hyperbolic geometry.

How to Picture Hyperbolic Geometry To think of any type of non-Euclidean math, you must

understand curvature. There are three types of curvature: flat curvature, positive curvature, and negative curvature. Flat curvature is what is it sounds like, something that is completely flat, having, in fact, no curve. Positive curvature is something that is curved the same way no matter what trajectory you take on it. An example of this is a sphere. That is why it is used in elliptic geometry. Negative curvature is something that curves differently depending on what path you take on its surface. For instance, a Pringle’s chip, or a saddle, features negative curvature. The curve of a saddle from the front to the back is pointed down.

However, from the right side to the left side, it is curved upwards. Hyperbolic math explores negative curvature.

Graphing hyperbolic, geometric shapes requires a Poincaré disc, a circular disc that has no boundaries.

On this disc, the further away from the center you travel, the greater the distance in the same amount of space. To create lines on a Poincaré disc, you have to make lines that are perpendicular to the “boundary,” giving lines that are considered straight on the disc a

seemingly curved look when represented in Euclidean space. Because these lines are seen as curved, this affects many important geometric concepts. For example, in Euclidean math, a triangle has an interior angle sum of 180º. However, in hyperbolic math, the “curved” lines make the angle sum of a triangle less than 180º. Similarly, the curves affect the idea that there is only one line containing point p that is parallel to line l. Technically speaking, being parallel is not necessarily defined as being equidistant from any point on the line. Instead, it is two lines on the same plane, not touching. Since the lines are not “straight,” there can be infinite parallel lines to one line, thus there can also be infinite lines containing point p that are parallel to line l.

Real World Implication The introduction of non-Euclidean math has opened

up many debates and questions to mathematicians, scientists, and students. One major question scholars attempt to answer even today pertains to our entire universe.

Is the universe Euclidean, hyperbolic, elliptic, or something else all together?

To attempt to answer this, scientists try to measure triangles. Silly as it seems, the interior angle sums of triangles are the key to explaining whether or not the universe is Euclidean. If the triangles’ angle sums measured in space are 180º, then they are Euclidean.

If they are less than 180º, the universe is hyperbolic, but if they are greater than 180º, it is elliptic. Try as we might, there has been no clear result in these tests, and we still do not truly know what type of world we live in. Ideas like gravitational forces and the Theory of Relativity may help us discover more about the shape of the universe. There is still much to learn from this math, and how we can use it to understand the world around us.

Fatou Mbaye Comment, Sami. “History of Hyperbolic Geometry.”

The Geometric Viewpoint, 8 Dec. 2016, web. point/2016/12/08/history-of-hyperbolic-ge ometry/.

Hyperbolic Geometry, Section 5, www.math.cornell. edu/~mec/Winter2009/Mihai/section5.html. http://.org/books/Book31/files/cannon.pdf

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KAKURO Puzzles

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Kakuro puzzles are like a cross between a crossword and a Sudoku puzzle.

Instead of letters, each block contains the digits 1 through 9. The same digit will never repeat within a word. If you add the digits in a word, the sum will be the number shown in the clue. Clues are shown on the left and right sides of “across” words, and on the top and bottom sides of “down” words.

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ISSUE #13

About Dr. Dragon Dr. Dragon is our school’s student produced magazine that focuses on math, science, and engineering. The mission of this magazine is to give HSMSE students the opportunity to take the school’s core subjects and explore subtopics that particularly interest them. Students on the magazine staff research and write about subjects of their choice. They are also involved with the production of the magazine, and learn about everything from design to fundraising and budgeting.

If you are an HSMSE student and want to contribute your thoughts, please talk to our officers or our faculty advisor, Mr. Choi.

Contact information: Dr. Dragon email: hsmsedrdragon@gmail.com Mr. Choi: RChoi@hsmse.org Also, you can read our previous magazines, and check the answers to crossword puzzles and Sudoku puzzles by visiting our website: https://drdragonathsmse.wixsite.com/website

Copyright © 2016 by Dr. Dragon All rights reserved. Published by Dr. Dragon No part of this publication may be reproduced or transmitted in any form by any means without prior written permission by the publisher.

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