2013_Mathematics in Our Life No. 1_Bucuresti_GicaVictor

Students Newspaper

First issue

Semester

Mathematics knows no races or geographic boundaries; for mathematics, the cultural world is one country. David Hilbert

MATHEMATICS IN OUR LIFE

Gheorghe Asachi Technical College

Students: Alexandru George Vasile, Claudia Mariana Stancu, Laura Vasilica Dinu, Bogdan Anton Croitoru, Daniela Ludat, Elisabeta Dumitrescu, Elena Alexandra Martin, Elena Tulea, Monica Florentina Ferenczi, Cristina Mihaela

Headmaster Adriana Stoica Assistant Headmaster Daniela Elisabeta

Editor Daniela ilic Editorial Secretary Victor Emanuel Gica

Inside this issue

How can Maths be so Universal? 2 The Science of Mathematics: What is it? .. 3 Maths of the Roulette. Blaise Pascal ....................... 5 Leonardo Fibonacci. Fibonacci Numbers in Botany 7 The Golden Ratio in Painting ...................................... 9 Mathematical Sculpture ............................................ 10 Maths in Nature ......................................................... 11 Fractals ... 12 Greek Mathematics .................................................... 13 Ancient Astronomy . 15 Exponential Word Problems ..................................... 17 Age Word Problem .................................................. 19 Maths Riddles .............................................................. 21 Maths Humor ... 22 Magic Square ............................................................... 23 Crossword Puzzle ....................................................... 24 Maths Study Skills Self-Survey ............................ 25 About Gheorghe Asachi ... 27

Human beings didnt invent maths concepts; we discovered them. Mathematics is the only language shared by all human beings regardless of culture, religion, or gender. With this language we can explain the mysteries of the universe or the secrets of DNA. We can understand the forces of planetary motion, discover cures for catastrophic diseases, or calculate the distance from Bucharest to London. We can make chocolate chip cookies or save money for retirement. We can build computers and transfer information across the globe.

Math is not just for calculus majors. It's for all of us. And it's not just about pondering imaginary numbers or calculating difficult equations. It's about making better daily decisions and, hopefully, leading richer, fuller lives.

Join us as we explore how math can help us in our daily lives!

Daniela ilic

The science of mathematics is a controversial subject among todays students. Their opinions are split and thus appeared two sides: the ones who enjoy mathematics and the ones who dont. Despite their arguments, there is one thing both groups have in common: their teachers and parents seem to insist on the fact that mathematics makes ones life easier and better. We will therefore try to answer the fundamental question that arises from the above mentioned affirmation: why? In order for this answer to be found, we must find the advantages that come from studying mathematics. Alas, we must look at its characteristics. One the first hand, we know that this science is a logic one. It revolves around deduction and systematic work. Even though it stands on theoretical grounds, it is impossible for one to achieve success while studying it without continuous exercise. Moreover, the discipline of mathematics is an exact one, which leaves little room for interpretations. If these exist, however, they are usually under the form of other exact and logic choices.

The Science of Mathematics: What is it?

Page 2

On the second hand, this science of mathematics splits a problem into the factors that composes it, while solving each one at a time, leading to a more precise and efficient solution.

On the third hand, we also know that mathematics cannot be done without a clear coordinated organization. Chaos has no room when studying this science. Finding a solution to anything tied to it will be nearly, if not impossible without having things ordered out. In the end, it is correct to assume that albeit the science of mathematics is complicated and can not be learned in a short time, the learning process is aided by the fact that everything related to it is logical and follows the same general path with few modifications.

Mathematics in Our Life Page 3

Laura Liliana Apostol

French inventor, Blaise Pascal was one of the most reputed mathematician and physicist of his time. He is credited with inventing an early calculator, amazingly advanced for its time. Pascal helps create two major new areas of research: he wrote a significant treatise on the subject of projective geometry , and later corresponded with Fermat on probability theory, strongly influencing the development of modern economics and social science.

Blaise Pascal

Maths of the Roulette

Page 4

Blaise Pascal created a formula to show the probability of two people winning in a casino game, and this has become the essence of probability theory! Now, at one time, when Blaise Pascal was trying to invent a perpetual motion machine, he invented Roulette instead! Pascal created the roulette wheel for a random number generator. After 200 years, in 1842, brothers Louis and Francois Blanc gave a new wheel design and added a single "0" increasing the house edge to 2.70%. Name of roulette (roulette) comes from French meaning "little wheel."

The American wheel has 38 numbers because of the additional double zero (00). The house edge in American wheel is 5.3 % due to this extra number.

When you flip a coin there are 2 possible outcomes: heads, tails. If you want to know what is the probability that the coin will come up heads, then that would be: heads / (heads + tails) = 1/2 = 0.5. Likewise when playing an even money bet at roulette, that option covers 18 of the 37 possible outcomes: 18/37= 0.48648649. To find out the effect the odds have on a measurable outcome, we can apply that outcome to all possible results. So if were playing $1 on black, then we know that for 18 of 37 outcomes we will net $1 profit, and for 19 of the 37 possible outcomes we will net a $1 loss. ((18/37)*1)+((19/37)*-1)=-0.02702703. This shows the house advantage on any single spin applied to your bankroll. We know that if you place $1 on any even number bet on avege you will loose almost three cents per spin or $27 over 100 spins.If you place a bet on one of the three options, then you are obviously playing against probability: 12/37= 0.32432432 probability to win.

Probability


"Lottery: A tax on people who are bad at maths."

Alexandru George Vasile

Fibonacci, or more correctly Leonardo da Pisa, was born in Pisa in 1175 AD. He was the son of a Pisan merchant who also served as a customs officer in North Africa. He travelled widely in Barbary (Algeria) and was later sent on business trips to Egypt, Syria, Greece, Sicily and Provence. In 1200 he returned to Pisa and used the knowledge he had gained on his travels to write Liber abaci (which means The Book of Calculations) in which he introduced the La-tin-speaking world to the decimal number system. The first chapter of Part 1 begins: These are the nine figures of the Indians: 9 8 7 6 5 4 3 2 1. With these nine figures, and with this sign 0 which in Arabic is called zephirum, any number can be written, as will be demonstrated.

Fibonacci is perhaps best known for a simple series of numbers, introduced in Liber abaci and later named the Fibonacci numbers in his honour. The series begins with 0 and 1. After that, use the simple rule: Add the last two numbers to get the next: 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987,...

Fibonacci Numbers

Leonardo Fibonacci

Page 6

Probably most of us have never taken the time to examine very carefully the number or arrangement of petals on a flower. If we were to do so, several things would become apparent. First, we would find that the number of petals on a flower is often one of the Fibonacci numbers. For example, the outer ring of ray florets in the daisy family

illustrate the Fibonacci sequence extremely well. Daisies with 13, 21, 34, 55 or 89 petals are quite common.

The Fibonacci number patterns encountered herein occur so frequently in nature that we often hear the phenomenon referred to as a "law of nature". The association of Fibonacci numbers and plants is not restricted to numbers of petals: the scale patterns of pinecones, the seed patterns of sunflowers and even the bumps on pineapples. Here we have a schematic diagram of a simple plant, the sneezewort. New shoots commonly grow out at an axil, a point where a leaf springs from the main stem of a plant.

Fibonacci Numbers in Botany


Claudia Mariana Stancu

Fibonacci numbers or the "law of nature".

In mathematics and the arts, two quantities are in the golden ratio if the ratio of the sum of the quantities to the larger quantity is equal to the ratio of the larger quantity to the smaller one. The golden ratio is an irrational mathematical constant, approximately 1.6180339887 . The Golden Raitio just like MATHS is used in everything.

At least since the Renaissance many artists and architects have proportioned their worksto approximate the golden ratioespecially in the form of the golden rectangle, in which the ratio of the longer side to the shorter is the golden ratiobelieving this proportion to be aesthetically pleasing. There is proven evidence that Leonardo Da Vinci used theories proposed by Fibonacci. In his famous painting, Mona Lisa, there seems to be a pattern to his work. Leonardo da Vinci ilustrates the mathematical proportions found in human anatomy as described in the Golden Section in the Vitruvian Man . The hexagram framing the Vitruvian Man is more perfectly shown in the pentagram of Pythagoras , which can be broken into Golden Rectangles .

The Golden Ratio in Painting

The Golden Ratio

Page 8

Art and Science just seem to be antagonistic concepts. In fact, we can find unique aesthetical qualities on several objective, rigid, geometric and mathematical shapes. One mathematical connection with art is that some individuals known as artists have needed to develop or use mathematical thinking to carry out their artistic vision. Another connection is that some mathematicians have become artists, often while pursuing their mathematics. Art is concerned with communication of emotions as well as beauty. Like art itself, the issues of beauty, communication, and emotions are complex subjects, but then so is mathematics.

Mathematical Sculptures George W. Hart: Mathematical yet organic, these abstract forms invite the viewer to partake of the geometric aesthetic.

Zachary Abel: I think about math constantly, and I see and look for math in everything around me. By transforming often-overlooked household items into elaborate, mathematical sculptures, I hope to share this sense of excitement, curiosity, and beauty that a mathematical

outlook has instilled in me.

Mathematical Sculpture


Laura Vasilica Dinu

Mathematics is everywhere in this universe. We seldom note it. We enjoy nature and are not interested in going deep about what mathematical idea is in it. Here are a very few properties of mathematics that are depicted in nature.

Parallel lines: In mathematics, parallel lines stretch to infinity, neither converging nor diverging.

Cones: A cone is a three-dimensional geo-metric shape that tapers smoothly from a flat, usually circular base to a point called the apex or vertex.

Hexagons: Hexagons are six-sided polygons, closed, 2-dimensional, many-sided figures with straight edges.

Self-similarity The idea of self-similarity occurs throughout nature the frond of a fern looks like the whole fern, a branch of a tree splits into further branches which look like trees themselves, and so on. Self-similarity now forms part of an area of mathematical research known as fractal geometry. Beautiful patterns can be generated by fractal formulas.

Maths in Nature

Page 10

Bogdan Anton Croitoru

A fractal is an object or quantity that displays self-similarity, in a somewhat technical sense, on all scales. The object need not exhibit exactly the same structure at all scales, but the same "type" of structures must appear on all scales. A plot of the quantity on a log-log graph versus scale then gives a straight line, whose slope is said to be the fractal dimension. The prototypical example for a fractal is the length of a coastline measured with different length rulers. The shorter the ruler, the longer the length measured, a paradox known as the coastline paradox. Koch snowflake

Gosper island Box fractal

Fractals


The origins of Greek mathematics are not easily documented. The earliest advanced civilizations in the country of Greece and in Europe were the Minoan and later Mycenean civilization, both of which flourished during the 2nd millennium BC. While these civilizations possessed writing and were capable of advanced engineering, including four-story palaces with drainage and beehive tombs, they left behind no mathematical documents. Though no direct evidence is available, it is generally thought that the neighboring Babylonian and Egyptian civilizations had an influence on the younger Greek tradition : Between 800 BC and 600 BC Greek mathematics generally lagged behind Greek literature and there is very little known about Greek mathematics from this periodnearly all of which was passed down through later authors, beginning in the mid-4th century BC.

Greek Mathematics

Page 12

Eudoxus of Cnidus

Eudoxus of Cnidus (410 or 408 BC 355 or 347 BC) was a Greek astronomer, mathematician, scholar and student of Plato. Since all his own works are lost, knowledge of him is obtained from secondary sources, such as Aratus's poem on astronomy.

Daniela Ludat

Thales of Miletus ( c. 624 BC c. 546 BC) was a pre-Socratic Greek philosopher from Miletus in Asia Minor, and one of the Seven Sages of Greece. Many, most notably Aristotle, regard him as the first philosopher in the Greek tradition. According to Bertrand Russell, "Western philosophy begins with Thales. Thales attempted to explain natural phenomena without reference to mythology and was tremendously influential in this respect. Almost all of the other Pre-Socratic philosophers follow him in attempting to provide an explanation of ultimate substance, change, and the existence of the worldwithout reference to mythology. In mathematics, Thales used geometry to solve problems such as calculating the height of pyramids and the distance of ships from the shore. He is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales' Theorem. As a result, he has been hailed as the first true mathematician and is the first known individual to whom a mathematical discovery has been attributed .


Thales of Milet

In the next issue: Pitagora and Arhimede

Ancient Greks had important contributions in astronomy. The first scientific contributions were associated to Thales of Milet and Pitagora of Samos , but none of thetir writings remained until nowadays. The legend in which Thales predicted the solar eclipse from 28th May 585 B.C.is probably miscredited . Around 450 B.C. , the Greeks started to study the planets movement. Pitolaus , an apprentice of Pitagora, thought that Earth , sun ,the moon and the planets rotated together around a central fire,hidden by another planet. Along with this theory ,the rotation around the fire was influenced by the daily movement of sun and the stars. In 370 B.C. astronomist Eudoxus of Cnidus explained this movement pretendnig the hipothesys that a giant sphere, which had in its centre the Earth , sustained the stars on its interior surface and it made a full rotation per day. In addition, to take into consideration the movement of sun ,the moon and the planets , he presumed that inside this star , the planets were related to many transparent spheres that rotated on different trajectories.

Ancient Astronomy

Page 14

Probably the most original ancient observer of the sky was the Greek Aristarh of Samos. He thought that the cosmic movements could be explained by the hipothesys that Earth rotates around his axes and, along with the other planets , they rotate around the Sun daily. This theory ,known as the geocentric system remained unchanged for 2000 years. In the second century A.D.. the Greeks combined their celestial theories with the observation of the planets . The astronomists Hipparchus and Ptolemeu determined the positions of a thousand stars and they used the map as a knowledge base in the measuring of the planetary movement. For a better system of circulatories orbits , we leave aside the spheres of Eudoxus , it appeared as a series of excentrical circles , spinning around a point near Earth to represent the movement to wards East , with different speed , of the planets around the horoscope.

The fact that each of the planets were steadily circling around a second circle , mamed epicicle , which centre was on tthe frst circle explained the periodical variations of suns and the moons speed.

Ancient Astronomy


Elisabeta Dumitrescu

A biologist is researching a newly-discovered species of bacteria. At time t = 0 hours, he puts one hundred bacteria into what he has determined to be a favorable growth medium. Six hours later, he measures 450 bacteria. Assuming exponential growth, what is the growth constant k for the bacteria?

Exponential Word Problems

Page 16

Exponential word problems almost always work off the growth / decay formula: A = Pekt

The units on time t will be hours, because the growth is being measured in terms of hours. The beginning amount P is the amount at time t = 0, so, for this problem, P = 100. The ending amount is A = 450 at t = 6.

450 = 100e6k 4.5 = e6k ln(4.5) = 6k ln(4.5)/6 = k = 0.250679566129...

The growth constant is 0.25/hour.

Note that the constant was positive, because it was a growth constant. If I had come up with a negative answer, I would have known to check my work to find my error.

Problem 1

A certain type of bacteria, given a favorable growth medium, doubles in population every 6.5 hours. Given that there were approximately 100 bacteria to start with, how many bacteria will there be in a day and a half?

Problem 2

Radio-isotopes of different elements have different half-lives. Magnesium-27 has a half-life of 9.45 minutes. What is the decay constant for Magnesium-27? Round to five decimal places.

Problem 3

A hepatobiliary scan of the gallbladder involved an injection of 0.5 cc's (or about one-tenth of a teaspoon) of Technetium-99m, which has a half-life of almost exactly 6 hours. Figure out just how much radioactive material remained from the gallbladder scan after twenty-four hours.

For you to solve!


Monica Florentina Ferenczi

Age Word Problem

Page 18

"Here lies Diophantus," the wonder behold . . . Through art algebraic, the stone tells how old: "God gave him his boyhood one-sixth of his life, One twelfth more as youth while whiskers grew rife; And then yet one-seventh ere marriage begun; In five years there came a bouncing new son. Alas, the dear child of master and sage After attaining half the measure of his fathers life chill fate took him. After consoling his fate by this science of numbers for four years, he ended his life." Find Diophantus' age at death.

His whole life had been divided into intervals which, when added together, give the sum of his life. So I'll add the lengths of those periods, set their sum equal to his (as-yet unknown) total age, and solve:

.d/6 + d/12 + d/7 + 5 + d/2 + 4 = d ( 25/28 )d + 9 = d 9 = d ( 25/28 )d 9 = ( 3/28 )d 84 = d Diophantus lived to be 84 years old.

Let d stand for Diophantus' age at death.

Problem 1

In three more years, Miguel's grandfather will be six times as old as Miguel was last year. When Miguel's present age is added to his grandfather's present age, the total is 68. How old is each one now?

Problem 2

One-half of Heather's age two years from now plus one-third of her age three years ago is twenty years. How old is she now?

Problem 3

The product of two consecutive negative integers is 1122. What are the numbers?

Problem 4

A garden measuring 12 meters by 16 meters is to have a pedestrian pathway installed all around it, increasing the total area to 285 square meters. What will be the width of the pathway?

For you to solve!


Alexandra Elena Martin

1. 27 ducks are marching to the pond. 5 lose their way, 13 return, and 9 of them make it to the pond. What happens to the rest of them?

2. So you think you're good at maths? Complete the sequence: 1=3, 2=3, 3=5, 4=4, 5=4, 6=3, 7=5, 8=5, 9=4, 10=3, 11=?, 12=?

3. In a certain country of 5 = 3. Assuming the same proportion, what would be the value of 1/3 of 10 ?

4. A woman has 7 daughters and they each have a brother, how many children does she have?

5. As I was going to St. Ives I met a man with seven wives. Each wife had seven sacks, Each sack had seven cats, Each cat had seven kits; Kits, cats, sacks and wives, How many were going to St. Ives?

Maths Riddles

Page 20

Solutions in the next issue! Cristina Mihaela Dinu

Maths Humor


Try to fill in the missing numbers. Use the numbers 1 through 9 to complete the equations. Each number is only used once. Each row is a math equation. Each column is a math equation. Remember that multiplication and division are performed before addition!

Magic Square

Page 22

Solution in the next issue! Elena Tulea

Across 3. He thought that Earth , sun ,the moon and the planets rotated together around a central fire. 5. Lines that stretch to infinity, neither converging nor diverging. 7. He illustrated the mathematical proportions found in human anatomy. Down 1. He created a formula to show the probability of two people winning in a casino game. 2. He introduced the Latin-speaking world to the decimal number system. 4. They are six-sided polygons. 6. He was the first to use deductive reasoning applied in geometry.

Crossword Puzzle


Have you read our articles?

This study skills survey is designed to help you review your current study habits and perhaps learn new ones. For each statement, choose the response that is closest to your current practices and attitudes: 1 - never, 2 almost never, 3 sometimes, 4 - almost alwayst, 5 alwayst.

Maths Study Skills Self-Survey Study Strategies for Maths Class

Page 24

1. I read my textbook before I come to class. 2. If I have trouble understanding the text, I find an al-

ternate text. 3. I take notes in math class. 4. I am careful to copy all the steps of math problems in

my notes. 5. I ask questions when I am confused. 6. I try to determine exactly when I got confused and

exactly what confused me. 7. I review my notes and text before beginning

homework. 8. I work problems until I understand them, not just until

I get the answer in the book. 9. I use flashcards for formulas and vocabulary. 10. I develop memory techniques to remember math

concepts.

After answering each statement, add the points to see how you did. Your score was 40 50: Give yorself a 10! You are using the study skills you need in order to be successful in maths. Your score was 21 39: You are probanly having a difficult time in maths class, but maths may not be your trouble! More than likely, your main problem is the study strategies you are using. Your score was 10 20: For you the maths class is certainly a nightmare! Make yourself do the things on this list. In the next issue: Maths tests

Get your grade!


THE MISSION OF OUR SCHOOL is to prepare individuals to be lifelong

learners in o world where the nature of work will constantly change over individuals lifetimes.

About Gheorghe Asachi

Gheorghe Asachi (March 1, 1788 November 12, 1869) was a Moldavian-born Romanian prose writer, po-et, painter, historian, dramatist and translator. An Enlightenment-educated polymath and polyglot, he was one of the most influential people of his generation. Asachi was a respected journalist and political figure, as well as active in technical fields such as civil engineering and pedagogy, and, for long, the civil ser-vant charged with overseeing all Moldavian schools. Among his leading achievements were the issuing of Albina Romneasc, a highly influential magazine, and the creation of Academia Mihilean, which replaced Greek-language education with teaching in Romanian.

Students NewspaperFirst issueSemesterMaths of the Roulette. Blaise Pascal ....................... 5Maths in Nature ......................................................... 11Fractals ... 12Greek Mathematics .................................................... 13Ancient Astronomy . 15Exponential Word Problems ..................................... 17Age Word Problem .................................................. 19Maths Riddles .............................................................. 21Maths Humor ... 22Magic Square ............................................................... 23Crossword Puzzle ....................................................... 24Maths Study Skills Self-Survey ............................ 251_issue.pdfPage #Mathematics in Our LifePage #Blaise PascalMaths of the RoulettePage #Probability Mathematics in Our LifePage #Page #Mathematics in Our LifePage #Page #Mathematics in Our LifePage #Self-similarity Maths in NaturePage #FractalsMathematics in Our LifePage #Greek MathematicsPage #Eudoxus of CnidusMathematics in Our LifePage #Thales of MiletIn the next issue: Pitagora and ArhimedeAncient Astronomy Page #Ancient Astronomy Mathematics in Our LifePage #Exponential Word ProblemsPage #For you to solve!Mathematics in Our LifePage #Age Word ProblemPage #For you to solve!Mathematics in Our LifePage #Maths RiddlesPage #Solutions in the next issue!Maths HumorMathematics in Our LifePage #Magic SquarePage #Solution in the next issue!Crossword PuzzleMathematics in Our LifePage #Maths Study Skills Self-SurveyPage #Get your grade!Mathematics in Our LifePage #

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2013_Mathematics in Our Life No. 1_Bucuresti_GicaVictor