
Have I gone insane? Mythbusting pentagons by compass & straight edge.
Posted:
Aug 8, 2013 6:25 PM


Can a regular pentagon with five identical side lengths and five internal angles of 72° be inscribed on a circle with compass and straight edge only?
Of course it can! Pentagons have appeared on coins for more than 2500 years.
Countless geometers over thousands of years have drawn perfectly regular pentagons on a circle with compass and straight edge!
Jonathan you are insane!!!
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OK. It's just that when I check, the published images of hand drawn pentagons inscribed on a circle with compass and straight edge only are always, well, wonky!
Have we enforced beauty on an irrational construction?
I have tried to draw the perfect regular pentagon on a circle with compass and straight edge and FAILED!
I have uploaded an early (slightly comical) video of me constructing a regular pentagon. It looks good, yet it's NOT regular!
https://www.youtube.com/watch?v=sqE1s1oUBsU
I can draw a regular pentagon around a clock face at 12 minute intervals. That's fun!
I know the mathematics works for a regular pentagon, yet I have looked at Euclidean and other pentagons and followed instructions.
We assume a regular pentagon can be drawn on a circle with straight edge and compass yet I can't and ALL the examples of published regular pentagons drawn by compass and straight edge on a circle have been wonky.
And yes, I'm looking at Eu kid!
So my request is, get out your geometry books and turn to the image of the pentagon handdrawn with compass and straight edge on a circle.
Measure the side lengths. Are they all consistent to 1 mm?
Some I've seen are out by 1 cm yet said to be regular.
Please give me proof they can be drawn. Don't TELL me SHOW me. Draw it! You can follow a method via this link... http://upload.wikimedia.org/wikipedia/commons/3/32/Regular_Pentagon_Inscribed_in_a_Circle_240px.gif
If you draw a regular pentagon on a circle BY HAND (not dynamic geometry software) with straight edge and compass, EXACTLY, please email it to me and put me out of my misery.
Otherwise I'll have to put in a request to MythBusters!
Thank you,
Jonathan Crabtree Mathematics Researcher Melbourne Australia (Currently over at http://bit.ly/Vrrx9Q)
P.S. I can email examples of wonky pentagons on request. As some highly respected geometers are still alive, I do not wish to cause them embarrassment.
P.P.S. Yes, I might be insane... But what if I'm not? My ruler has no vested interest.
P.P.S. My 'comedic' YouTube video is unlisted and may be pulled shortly to spare me further grief! https://www.youtube.com/watch?v=sqE1s1oUBsU

