Irrational Number A to Z

Irrational Number
A to Z

By Jaesung, Bomin, Jaewoong, & Yoonjea ��from Deogweon Middle School

Table of Contents

1. Historical Background --
2. Mathematicians --------
3. Myth & Fact ------------
4. Cases -------------------
5. Book Review ------------
6. Math around us --------
7. What we learned -------

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Before we get started,

Jaesung
This is my very first experience making an e-book but I will try my best to make the best e-book.

Bomin
I'm not good at math at all but I'll work together with my team as much as I can.

Jaewoong
I think solving math questions for my math class is not fun but creating e-book about math is so fun and I hope I can get to like Math after this activity.

Yoonjea
Due to Covid19, I didn't see my friends often but I think this project will help me to work with friends. I will work hard on this.

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1. Historical Background

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Around the 6th century BC, the Pythagorean school, centered on Pythagoras, believed that numbers could only be expressed as integers or ratios of integers (fractions). One day, when one of the Pythagoreans, Hippasos, was looking for the ratio of each line segment that makes up a figure, he drew a square of length 1 and drew a diagonal. there was no So, solving with the Pythagorean theorem, a²=2, 1.414213… … A prime number that does not cycle with . So this fact is reported to the people of the school, but the people of the school don't believe it and instead kill Hippasus.

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After that, in the 7th century India, the irrational number found by Hippasos was finally recognized, and at first, irrational numbers such as ka15 and ka10 were expressed instead of the root symbols we know. After some time, the symbol √ was created by taking the r from the Greek word radix, which means root. Then, around 1500, French mathematician Descartes began to think about how to change √. The reason is that it is difficult to see at a glance how far √ is applied. So, Descartes added horizontal bars until he wanted to express the square root. By creating this symbol, the scope of application of the route has been increased.

2. Mathematicians

1. Archimedes

Archimedes invented the concept of infinite primes in an era when there was no modern integral. An approximation was found using the elimination method, and was calculated using a regular decagon.

According to a famous story, when there were rumors that the king's crown had been mixed with other substances, he summoned Archimedes to find out. When he entered the bathroom, he saw the water overflowing from his body and accidentally discovered the principle of buoyancy, and exclaimed, "I found it, Eureka!

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2. Hippasus

By applying the Pythagorean theorem, the theorem named after his teacher, to a right-angled triangle with two sides of length 1, Hippasus discovered the number √2, proving that it is a number that cannot be expressed in a perfect integer ratio. At that time, the Pythagoreans believed that the origin of all things was a natural number, and taught that all numbers can be expressed as ratios of natural numbers. In other words, the existence of irrational numbers implied the Pythagorean error. So he was killed by the Pythagoreans.

3. René Descartes

Descartes was a mathematician of the 17th century who accomplished many great achievements in science and philosophy as well as essential in mathematics, such as the use of the coordinate plane and the unknown x. It is also famous for simply solving the inconvenience of the old √.
As his representative story, Descartes, who was thinking while lying in bed, looked at the fly on the ceiling and wondered if there was any way to indicate the location. So what he thought was the coordinate plane. He drew two lines that meet each other on the ceiling, and called these two lines the horizontal and vertical axes, respectively. The position of the fly could be indicated by the values of the horizontal and vertical axes.

Let us find the timeline of the mathematicians we researched so far.

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Let us find the timeline of the mathematicians we researched so far.

Timeline of Mathematics – Mathigon

3. Myths & Facts

1) The Number of Petals and Leaves

Irrational numbers in the Fibonacci sequence

Leonardo Fibonacci studied this number, referring to the breeding of rabbits in 1202. It was Fibonacci who made an achievement to study and systematize this sequence in Western Europe, hence the name Fibonacci sequence.
The Fibonacci sequence includes 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, etc.
At this time, when I find the ratio between these numbers, it gradually becomes an irrational number and eventually comes out as an irrational number as the golden ratio.