Mathematica 2015

Mathematica 2015

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DCM ATHEMATICA 2015

E DITORS Zihan Zhou Zhengyuan Zhu

Junxiao Shen S UPERVISOR Dr Purchase

C OVER D ESIGNED B Y Zhengyuan Zhu & Zihan Zhou

A RTICLE C ONTRIBUTORS

Alex Boiardi

Henry Bradley

Alexander Cartwright

Andrew Hong

Keesje ’t Hooft

David Jaffe

Leslie Leung

Zeb Micic

Mr. Ottewill

Jan Rybojad

Junxiao Shen

Xiaofeng Xu

Andy Zhang

Zhengyuan Zhu

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E DITORS ’ N OTES

It is the time to look forward to Founder’s Day this year, whose theme is Persistence and Endurance. 2015 is the 100 th anniversary of Shackleton’s Great Imperial Trans Antarctic Expedition. Not surprisingly, this year’s DC Mathematica is tightly linked to the great spirits of a large number of mathematicians who devoted their whole lives to discover and explore mathematical principles behind simple questions. A large group of boys in the College have developed great enthusiasm to extend their vision beyond the syllabuses and they have made impressive progress. Not limited by their age, they eagerly show their discoveries by writing essays or short articles. During the editing process, we have received a considerable amount of articles and we have included some interesting mathematical puzzles for you to play with. Due to the limited length of this magazine, we are sorry that we cannot include all scripts we have received. Also thank you to Dr. Purchase for organising the editing again this year.

T HE E DITING T EAM . 9 TH J UNE 2015

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C ONTENTS Fooled by Randomness.............................................................1

By Zhengyuan Zhu (Y12)

Game Theory .............................................................................5

By Henry Bradley (Y13)

Latin in Mathematics...............................................................10

By Zeb Micic (Y8)

Markov Chain in Shackleton’s Voyage..................................12

By Andy Zhang (Y12)

Dr. Purchase’s Multiplication Problem.................................16

By Alex Boiardi (Y9)

Persistence and Endurance ....................................................18

By Junxiao Shen (Y12)

Coding in Mathematics ...........................................................22

By Andrew Hong (Y8)

Reflections on Reflections......................................................23

By Mr. Ottewill

Shackleton, Sextant and the…quadratic regression ...........25

By Jan Rybojad (Y12)

The Golden Ratio....................................................................33

By Alexander Cartwright (Y8)

Are Fourier Series of great importance?..............................34

By Xiaofeng Xu (Y13)

The Pancake Problem .............................................................41

By Keesje 't Hooft (Y13)

Triangle and Square .................................................................46

By David Jaffe (Y9)

What is the God's Number of the Rubik's Cube?..............47

By Leslie Leung (Y13)

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Fooled by Randomness

----Zhengyuan Zhu (Y12)

“Humans are often unaware of the existence of randomness. They tend to explain random outcomes as non-random. ” 1

People don’t understand how things are just random and try to make sense out of them. They would be making models out of stock >Page 1 Page 2 Page 3 Page 4 Page 5 Page 6 Page 7 Page 8 Page 9 Page 10 Page 11 Page 12 Page 13 Page 14 Page 15 Page 16 Page 17 Page 18 Page 19 Page 20 Page 21 Page 22 Page 23 Page 24 Page 25 Page 26 Page 27 Page 28 Page 29 Page 30 Page 31 Page 32 Page 33 Page 34 Page 35 Page 36 Page 37 Page 38 Page 39 Page 40 Page 41 Page 42 Page 43 Page 44 Page 45 Page 46 Page 47 Page 48 Page 49 Page 50 Page 51 Page 52 Page 53 Page 54 Page 55 Page 56 Page 57

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