# "Ancient Greek Geometry"--interactive puzzle

Main post link -> http://sciencevsmagic.net/geo/

I found this fun interactive Javascript game/puzzle that teaches concepts related to straightedge and compass constructions, and I thought I'd share it here. It's deceptively simple, and quite challenging. The best part about it is that because your constructions are encoded as an HTML link, you can share your solutions with others simply by copying the web address. Can you construct a regular pentagon in 15 moves or less? And can you construct other regular polygons that are not shown in the challenges, like the 15-gon and 17-gon?

http://sciencevsmagic.net/geo/

Also, check out the author's website for other interesting mathematical "toys."

Note by Hero P.
7 years, 1 month ago

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Remember to wrap math in $$ ... $$ or $ ... $ to ensure proper formatting.
2 \times 3 $2 \times 3$
2^{34} $2^{34}$
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\frac{2}{3} $\frac{2}{3}$
\sqrt{2} $\sqrt{2}$
\sum_{i=1}^3 $\sum_{i=1}^3$
\sin \theta $\sin \theta$
\boxed{123} $\boxed{123}$

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Try finding efficient constructions for all constructable regular polygons of 20 or fewer sides: these are $n \in \{ 3, 4, 5, 6, 8, 10, 12, 15, 16, 17, 20 \}.$ Some of the ones I've devised use some interesting tricks, because in practice, an actual compass would permit the transfer the length of a given line segment onto any other line in a single move.

My record for constructing the regular heptadecagon (17-gon) is 59 moves. Can anyone beat it?

- 7 years, 1 month ago

Nice Construction Puzzle . Thanks ! Found construction for n-gon with n = 3,4,5,6,8,10,12,16,20 .

for 15-gon , In wikipedia nice construction given ( pentadecagon ) . Note that by this method (to draw angle 36 ) , we can draw 20-gon, decagon and pentagon in less moves then in my method .

Still did not found method for 17-gon .

Circle Packing:- 2-i , 2-ii ,

3 ,

4 ,

7 .

- 7 years, 1 month ago

To give you an idea of more efficient constructions, here is my 16-gon using 31 moves. Note that extending a previously drawn line does not cost any additional moves.

One should also try to verify the correctness of the construction; this should be easy for most regular polygons.

- 7 years, 1 month ago

_ Interesting and Creative ! _

I saw that in your construction while making degree 22.5 , you were not only   try to make angle at one place then paste it at other places , but construct  same angle in many places together ,which leads to less moves .


Here is my method to make $36 ^ \circ$which used in making four constructions of n-gon . constuction of degree 36

_Curious to see idea of making 17-gon . _

- 7 years, 1 month ago

Thank you.

- 7 years, 1 month ago

This is so cool!

- 7 years, 1 month ago

Thanks Hero! It's really great!!!

- 7 years, 1 month ago

Thanks, this game is awesome!!

- 7 years, 1 month ago

This is awesome! Thanks!

- 7 years, 1 month ago

You cannot copy lengths with this, can you? I think that is allowed with construction? (by simply keeping the pair of compasses in that position)

- 7 years, 1 month ago

You are correct; the rules do not allow direct copying of lengths--you must find some other way to do it.

- 7 years, 1 month ago