Math

MATHEMATICS EXTENDED ESSAY

“Mathematics in Art”

Damla Şenol
D1129057
Session: May 2010
Supervisor: Deniz Candemir
TED Ankara Collage Foundation High School

ŞENOL Damla D1129-057

ABSTRACT
Mathematics is one of the most important, beneficial and effective study, all over the world.
Art is also has a great importance on a society as it includes visuality, emotions and creativity.It is thought that mathematics and art completely different kinds of studies, they have a strong
interaction. As mathematics has an important role, its one of the use is in arts. The question
that was researched and was used in this study is that “In what ways, does arts be affected by
mathematics?” In this study, Fibonacci Numbers, Golden Ratio, Carla Farsi and the Music are
studied.First of all, after my researches, I agreed that Fibonacci Numbers and Golden Ratio are the
most common relations between maths and art. These two, are not only related with arts, also,
we can find them in our daily life, easily. These mathematical tools were used by lots of
artists, for example Leonardo da Vinci. This study is exactly focused on the applications of
these on arts. The applicationsof these two on other areas are also studied, basically, to
emphasize their importance on life. The use of mathematics and also, to prove my study,
Carla Farsi who is both a mathematician and an artist, are studied.

By taking all these points into consideration, the ways that arts is affected by mathematics and
also, their relations are showed in this study.

Word Count : 230

2ŞENOL Damla D1129-057

CONTENTS
Abstract ……………………………………………………………………………………….2
Research Question …………………………………………………………………………....4
1. Introduction .......................................................................................................................... 4
2. The Fibonacci Sequence and the Golden Ratio ................................................................. 4
2.1. TheFibonacci Sequence.................................................................................................. 4
2.2. The Golden Ratio and its Applications ........................................................................... 5
2.2.1. The Golden Ratio ..................................................................................................... 5
2.2.2 The Golden Ratio In GreatPyramid of Giza............................................................. 7
3. An Artist and a Mathematician: Carla Farsi .................................................................. 10
4. Maths in Music ................................................................................................................... 11
5. Conclusion........................................................................................................................... 13
6. Bibliography ....................................................................................................................... 15

3

ŞENOL Damla D1129-057

RESEARCH QUESTION :
In what ways, does arts be affected by mathematics?

1. INTRODUCTION

Mathematics and Art are the two different kinds ofstudies but there is an interaction between
them. As many people think that they are opposed to each other, they have a connection and
in arts, mathematical tools are used.

When you examine a human body, do you see a math in it? Most probably you don’t.
However, there is a golden ratio between the length of your face and the width of your
face. The same ratio is used in arts, for example, inpaintings. With these ratios or sequences,
it can be declared that the art and the math appear together.

In this essay, under the question; “ In what ways, does arts be affected by mathematics? ”, the
Fibonacci sequence and the Golden Ratio will be introduced with the examples of arts using
this structure, Carla Farsi who is both a mathematician and an artist. Also, it will be
introduced...