Real Mathematics – Life vs. Maths #1

Circle-Match Relationship

Mathematics is a language we use to explain the event that occur in nature. Mathematicians (good ones though) are in a way masters of this language. They possess crucial abilities such as seeing things others can’t see and finding connections between things that seem unrelated with one another.

Contrary to popular belief “knowing mathematics” doesn’t only mean knowing how to make calculations or being good with numbers. A mathematician ought to point out and explain the relationship, symmetry and pattern… In places you wouldn’t even imagine mathematics could exist!

For instance it is possible to use mathematics and find a connection between a circle and a match.

Circle

Let me start with circle. Any straight line segment that passes through the center of the circle with its endpoints lie on the circle is called a diameter of the circle. And in any circle the shortest distance between its center and boundary is called a radius of the circle. A radius is half the length of a diameter.

To draw a circle with a compass is not that hard. Distance of the openness of the compass gives the radius. If one opens a compass with 3 cm, he/she will draw a center that has radius 3.

Circumference of the circle above is roughly 18,85 cm. Let’s use a calculator to find the relationship between the diameter and circumference of this circle.

img_4642

18,85/6=3,141666666…

Now let me use a cup. This cup’s mouth is in a circle shape and its circumference is about 25,8 cm.

Its diameter is about 8,2 cm. Now let’s divide the circumference with its diameter:

img_4639

25,8/8,2=3,14634146…

In both examples ratio of circumference of a circle to its diameter is roughly 3,14. This is not a coincidence; humans realized this connection more than 4000 years ago.

Brief History of the Mysterious Number

2000 BC: Humans thought that this ratio as 3. According to the Rhind papyrus from ancient Egypt it was 3,16045.

250 BC: Ancient Greek Archimedes calculated this ratio’s average as 3,1418.

800 BC: Al-Khwarizmi calculated the ratio as 3,1416 which was a better approximation than Archimedes’.

Mathematicians didn’t stop attempts for thousands of years. In 1874 William Shanks found the first 707 digits of this ratio. Unfortunately he made a mistake on the 528th digit. Nevertheless it was a huge accomplishment to find this ratio’s first 527 digits correctly.

In 1949 computers took over the mission. A computer found this ratio’s first 2000 digits correctly.

pi2000

I tried it find if I could find the number “1907” (the year when my favorite team was founded) inside those 2000 digits. It was a success.

In the 18th century Leonhard Euler who is known as one of the greatest mathematicians of all times gave this ratio its name and symbol: π.

Transcendental

In 1882 a German scientist named Ferdinand von Lindemann proved that the number π is transcendental.

According to great German philosopher Immanuel Kant a transcendental knowledge is not real; it exists only in our minds. Majority of the mathematicians agree that this word defines the number π perfectly.

In other words the number π can’t be shown as the ratio of any two rational numbers.

Also in the decimal presentation of the number π continues without any repetition… Forever!

This means that every number combination can be found inside the number π. From your birthday to your elementary school number, everything is inside the number π. All you need to do is to continue calculating its digits.

Find Your π Day

This website is created by Wolfram. Using its searching engine you can find at what digit your birthday sits inside the number π.

I checked Leonhard Euler’s birthday and found the following:

eulerpi

Try and see yourself. It is astonishing to see your birthday inside the number π.

M. Serkan Kalaycıoğlu

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