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Star

RE: Star

Your solution is invalid since it implies that the two R2's are the same length and it's obvious from your diagram that they are not. Also, to what purpose are the R1's? They look like they play no role whatsoever in the answer.

John R. Baker, P.E. (ret)
EX-Product 'Evangelist'
Irvine, CA
Siemens PLM:
UG/NX Museum:

The secret of life is not finding someone to live with
It's finding someone you can't live without

RE: Star

I'm afraid the contruction is indeed incorrect (though R1 does play a role, it is to find R/2).
R2 should be the side of a pentagone, in that case its value would be R2=2R sin 36°=~1.176 R
But from the construction R2=√(R2+R2/4)=~1.118 R

prex
http://www.xcalcs.com : Online engineering calculations
http://www.megamag.it : Magnetic brakes and launchers for fun rides
http://www.levitans.com : Air bearing pads

RE: Star

Yea, that works pretty good...

John R. Baker, P.E. (ret)
EX-Product 'Evangelist'
Irvine, CA
Siemens PLM:
UG/NX Museum:

The secret of life is not finding someone to live with
It's finding someone you can't live without

RE: Star

(OP)
My error... left out a step.

RE: Star

I'm still not completely convinced what's the significance of the two 'R1' radial curves, unless their only purpose was to help find the mid-point of the horizontal line from the arc's center to its perimeter. So if that IS the case, then their lengths, 'R1', has NO relationship whatsoever to either the values of 'R2' and 'R3', correct?

John R. Baker, P.E. (ret)
EX-Product 'Evangelist'
Irvine, CA
Siemens PLM:
UG/NX Museum:

The secret of life is not finding someone to live with
It's finding someone you can't live without

RE: Star

Bingo! Now it's exact.
As before R2=√(R2+R2/4)=R√1.25
Now R3=√(R2+(R2-R/2)2)=R√(2.5-√1.25) and this is exactly 2R sin 36° !
However I admit that this is not a very elegant proof, another one based on pure geometry would be much better.

RE: Star

(OP)
That's correct, John. R1 is to determine the bisector of the line.

Dik

RE: Star

It's a classical Euclidean geometric proof, i.e. you need to prove the solution using only a straightedge (no markings allowed on it) and compass.

RE: Star

Of course with today's CAD packages, these sorts of things have trivial solutions when using their 2D sketch tools with a constraint-solver. BTW, this is how I would approach the problem of the two-ladders in an earlier 'Brain Teaser'.

John R. Baker, P.E. (ret)
EX-Product 'Evangelist'
Irvine, CA
Siemens PLM:
UG/NX Museum:

The secret of life is not finding someone to live with
It's finding someone you can't live without

RE: Star

maybe I'm dumb today but why does R3=2*sin36deg make it so ? don't we need the vertical distance of the R3 intersect with the datum circle ? (=x, then cos72 = (1-x)/R3)

another day in paradise, or is paradise one day closer ?

RE: Star

yes, I was dumb, but today I did some thinking and realised ... look at the centre !

another day in paradise, or is paradise one day closer ?

RE: Star

A 5-pointed star (pentagram) is a trivial variation of a pentagon.

Euclid's Method on Wiki with Animated Gif

Now that we've all finished inscribing our pentagrams, how long until somebody starts screaming "Witches!! Witches!! Witches!!" ?

RE: Star

"witches?" ... "burn 'em!"

another day in paradise, or is paradise one day closer ?

RE: Star

But how do you know she's a witch?

----------------------------------------

The Help for this program was created in Windows Help format, which depends on a feature that isn't included in this version of Windows.

RE: Star

She's got a wart!

RE: Star

She turned me into a newt

RE: Star

I got better.

----------------------------------------

The Help for this program was created in Windows Help format, which depends on a feature that isn't included in this version of Windows.

RE: Star

what do you do with witches ? (we can keep this going for weeks !)

another day in paradise, or is paradise one day closer ?

RE: Star

Yes, but I don't have to look it up, I've memorized the entire dialog. I've got a book of the screenplay which starts off in typical Python fashion with something completely different.

What a complete waste of my remaining brain cells!

----------------------------------------

The Help for this program was created in Windows Help format, which depends on a feature that isn't included in this version of Windows.

RE: Star

Always wondered...why the focus on pentagrams, when witches were supposed to put hexes on people?

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