SHOW me don't TELL me! I want to try! You're too young to play with a compass Jonathan ...
"One of the most beautiful results in all of Euclid's elements is the construction of a REGULAR PENTAGON inscribed in a circle. (Book IV Prop. 11)"
OK I'm all grown up and at age 52, I actually believed all that hype about compass and straight edge construction of a regular pentagon (and everything else!)
Yes the proofs work. Yes the math works.
Yet published pentagons drawn by compass and straight edge (by which I mean intersection of arcs) ALL appear to be wonky, yes WONKY!
I know 'wonky' is not as precise as equilinear and equiangular, yet 'wonky' expresses my child-like disappointment felt upon discovering the truth about Santa and the Easter Bunny.
There seems to be growing circumstantial evidence that the construction of a REGULAR pentagon by compass and straight edge is simply too hard.
When a world-famous geometry professor draws a 'regular' pentagon with compass and straight edge (according to Euclid) and one side is 30 mm and another side is 37 mm - well, I'm ALMOST prepared to declare REGULAR (accurate) pentagon construction by compass and straight edge a MYTH.
> 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!!! > > ============== > > 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 hand-drawn 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/Reg > ular_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 > Myth-Busters! > > 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