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Irrational Number A to Z

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By Jaesung, Bomin, Jaewoong, & Yoonjea ππfrom Deogweon Middle SchoolTable of Contents

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.

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

**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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Bomin

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

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.

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.

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.

Table of Contents

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.

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

**1. Historical Background --**

**2. Mathematicians --------**

**3. Myth & Fact ------------**

**4. Cases -------------------**

**5. Book Review ------------**

**6. Math around us --------**

**7. What we learned -------**

04

06

10

14

20

22

24

06

10

14

20

22

24

Bomin

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

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.

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.

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.

**5**

1. Historical Background

**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, aΒ²=2, 1.414213β¦ β¦ 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.

<Image Source: http://www.kdnews.co.kr/20347>

**CAPTION**

*Half page image nullam nunc eros, vehicula feugiat*

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 β 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 β. The reason is that it is difficult to see at a glance how far β 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.

**5**

1. Historical Background

**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, aΒ²=2, 1.414213β¦ β¦ 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.

<Image Source: http://www.kdnews.co.kr/20347>

**CAPTION**

*Half page image nullam nunc eros, vehicula feugiat*

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 β 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 β. The reason is that it is difficult to see at a glance how far β 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.

7

**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!

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!

**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 β2, 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.