A side of a polygon is 2a× sin(180/n) where n is the number of sides of a polygon.
When I drew a pentagon I used the formula
Root(2) - (3/4)(Root(3) - Root(2)). This requires only a compass. 1.175 is the side length of a pentagon if radius is 1.
Then I read in Wikipedia that as a kid Gauss drew a heptadecagon (17 sided polygon) using a compass. The full name of Gauss is Johann Carl Friedrich Gauss. Gauss was a child prodigy and made contributions due to which he is considered "the greatest mathematician since antiquity". He was also called "the foremost of all mathematicians". The erstwhile cgs unit of magnetic flux density was named after him. Gauss. Many web sites over internet say Gauss is the "Prince of Mathematics". And the "King of Mathematics" is Leonhard Euler.
Well I tried the adaptation of heptadecagon with a formula similar to pentagon.
(Root(14) - (3/4)(Root(15) - Root(14)))/10. Dividing by 10 needed here. (This cannot be obtained with compass. Dividing by 10) In a pentagon 5 you had 2 & 3. For heptadecagon 17 you have 14 and 15. The value is 0.364 while actually the value is 0.367. The side length of heptadecagon if radius is 1.
So a similar formula for both pentagon and heptadecagon exists. However dividing into 10 is not possible with a compass only. One needs setsquares or drafter. Anyway this method of mine needs a very large paper.
When I drew a pentagon I used the formula
Root(2) - (3/4)(Root(3) - Root(2)). This requires only a compass. 1.175 is the side length of a pentagon if radius is 1.
Then I read in Wikipedia that as a kid Gauss drew a heptadecagon (17 sided polygon) using a compass. The full name of Gauss is Johann Carl Friedrich Gauss. Gauss was a child prodigy and made contributions due to which he is considered "the greatest mathematician since antiquity". He was also called "the foremost of all mathematicians". The erstwhile cgs unit of magnetic flux density was named after him. Gauss. Many web sites over internet say Gauss is the "Prince of Mathematics". And the "King of Mathematics" is Leonhard Euler.
Well I tried the adaptation of heptadecagon with a formula similar to pentagon.
(Root(14) - (3/4)(Root(15) - Root(14)))/10. Dividing by 10 needed here. (This cannot be obtained with compass. Dividing by 10) In a pentagon 5 you had 2 & 3. For heptadecagon 17 you have 14 and 15. The value is 0.364 while actually the value is 0.367. The side length of heptadecagon if radius is 1.
So a similar formula for both pentagon and heptadecagon exists. However dividing into 10 is not possible with a compass only. One needs setsquares or drafter. Anyway this method of mine needs a very large paper.
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