ζ 60Stars Astrology Mini Appendix of Off Season 2～ ① Looking for a regular polygon whose length & area are integers！

60stars astrology

English version

By Tokyo-Tanuki

60stars Astrology Off- Season 2

ζ　 Mini Appendix of  "Off Season 2"　

1. Looking for a regular polygon whose length & area are integers！

1. Now, today is the day to write the mini-appendix, i.e., the day to write Tanu-chan's fantasy ‼

As I have said many times, I likes to be delusional.

For the past week or so, one thing has been on my mind, and I've been calculating it all the way on the commuter train.

Well, what I was doing was calculating the relationship between the length of one side of a regular polygon and the area of a regular polygon, up to 200 angles. ....

Oh! 
The lady sitting next to me has moved to another car !!



2. It is very difficult to do these calculations with a normal calculator, so I used a website called “KEISAN” operated by the famous Casio Computer Co.

This site is very useful and I recommend it.

As I drew in the picture at the top of this blog, you enter the length of one side of a polygon (e.g., A＝100) and calculate the area of a regular polygon (regular triangles to regular 200-sided polygons) !

At first, Tanu-chan was interested in how many cases the area would be an integer if the length of one side is "A" and "A" is a 3-digit number.

For example, if 100 is the length of one side（A＝100）, the area of a regular quadrilateral is an integer (10000), but the areas of other regular polygons are not.

I thought it would be a piece of cake if the length of one side  was 120, but this was also true only for regular quadrilaterals, where the area was an exact integer.

How about 124 or so? 

I tried this as well, but there were no other cases except for regular quadrilaterals.

🌟　🌟　🌟　🌟　🌟

3. Well, then, I tried to make the number of one side smaller.

I tried "A=4", that is, if one side is 4, I wondered what the result would be, but the area is not an integer except for a regular quadrilateral.

How about if "A=1" ?　
But again, the area of the polygon is not an integer except in the case of a regular quadrilateral.

I tried A=2, 3, 5, and 7, but again, the area is not an integer except in the case of a regular quadrilateral.

I made "A" larger, 1260, or 240, and it was the same!

...WHY?

Oh My God!!!

I haven't noticed that in at least 45 years!

🌟 🌟 🌟 🌟 🌟 🌟

While I was calculating like this, the train arrived at Ueno station, so I stopped calculating and got off the train.

Today's fantasy didn't go so well. ........

Now, what shall I calculate tomorrow  💛

Tanu-chan💓  TOKYO-TANUKKO💛