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I am sorry, I thought you only wanted a hint.

If you use the Pythagorean theorem you will get:

Take the square root of both sides.

]]>Regular means all internal angles and all sides are equal.

Bob

]]>I searched this topic in Google but I couldn't find anything discussing this topic. This is a pure work of mine. But I don't know if its completely true, somewhat OK or completely a wrong concept.

This is why I'm sharing it here so that you expert guys will share your thoughts on this, resulting in the correction of mine (or anyone else).

<This is a part of a blog post on my personal blog, so I'm just copying the necessary part of my article>

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My Personal Idea

Truly speaking, I didn’t read this anywhere so far. May be someone already discusses this aspect. But still I want to share:

Can you answer what’s zero? Let’s start counting the number of eggs you have in your refrigerator. Suppose, you’ve 3. You eat daily, an egg, then tomorrow, you’ll have 2, then on the day after tomorrow you’ll have one…At the last, you’ll have NO EGG. Now, how you’ll denote this fact mathematically?

To show that we’ve no egg, we will write it that we’ve zero eggs. Zero is basically a number that represents absence of mathematical objects.

Similarly, I feel, a point is to geometry, as Zero is to algebra, empty set is to set theory.

If I ask you, what’s 9 minus 9, what’ll be your answer? Obviously, you’ll say zero.

Similarly, while talking about set theory, if intersection of two or more sets is nothing (empty) we denote this fact by an empty set. Now, physically no empty set exists.

Then I feel, what’s the answer of this geometric problem, a line segment AB minus an equal measure of line segment DE? I’m trying to find the answer of this question, but naturally, I’m inclined to say that it must be a point! Because point has no dimensions, again, a point is to geometry, as zero is to algebra.

Now if you put several zeros on the right of some non zero number, e.g. 9, then it becomes a bigger quantity, e.g. 9,000.

But what about if you put several points together with either one another, or with some line? Obviously, several points together will form a line. Moreover, if you add more points on either to left or right side of a finite line, it’ll start extending indefinitely along left or right direction, respectively (which is one of the five postulates of Euclid).

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**A says) An equilateral triangle with sides 1.**

**B says) Obviously it is a triangle with the longest side being equal to 1.**

**C says) What is a unit?**

**D says) It is a triangle with an area that equals 1.**

**E says) I have never heard of it.**

**What do you say?**

9. A triangle ABC

The angles achieve the following relationship :[Sin(A)]^2+[Sin(B)]^2+[Sin(C)]^2=2

what kind of this triangle?]]>

the gray area is 3( r^2 - 1/4 π r^2)

the pink area is 1/4π r^2 -(π-3) r^2

= r^2(1/4π-π+3)

=r^2(-3/4π+3)

=3 r^2(1-1/4π)

=3(r^2-1/4π r^2)=the gray area

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That is correct! Very good.

]]>I hope for more of these in the near future.

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