gavinksong

That's actually really interesting. Thank you. I learned something new today.

Well, to be more explicit...

I had to think about this point: does it matter there are only n-1 rays? That's an excellent question.

Edit - corrected a sign error.

Um. It seems my answer isn't being addressed. I don't know why, but I apologize if I did anything wrong. Let me try to reword my previous answer in a more familiar context. Please hear me out.

These are impossible!

I think that's what I did above, except instead of solving for a radius, I solved for a vertex. However, I use "the math" mainly as a proof of concept for a method where a specific solution can be found out using a straightedge and a compass.

But that is correct. Well done! I'm sorry about the first stanza. This was my first attempt at a riddle.

to answer the spoiler question, i believe the circle radius needs to be greater than (equal) 1/2 the distance between two points. This is not true. You must mean that the sum of the radii of the two points in question needs to be larger than the distance between the points. To know what the appropriate radii are is equivalent to knowing the length of each side. TSLF never showed how he found these lengths, yet his solution depends on knowing them. If you don't believe me, imagine trying to reconstruct a triangle using TSLF's method. Unless you know beforehand what the side lengths are, you will probably have to do a lot of trial and error to find radii that lead to a sensible reconstruction.

This is my first ever riddle. It was inspired while reading a riddle by bonanova inspired by a series of riddles by plasmid. I hope you like it. I am a place where dead men lie And rows of earthen tablets remember. My callers may question life or cry But sadness I can temper. Silence is given in solemn respect To those who are my patrons. Your eventual return I do expect Come your expiration.

Bain is a word

I just found this thread, and I think I can come up with a simpler proof.

Interestingly, this also means that the midpoints of the sides of any quadrilateral are the vertices of a parallelogram. It also suggests that reconstruction of a triangle is always possible.

I think it is possible to reconstruct the pentagon (unless we can show that a solution is not unique), but I don't think TSLF's solution would work for all cases. Like BMAD said, what if the pentagon is not regular?

I think I'm the one who is at fault.

Bain isn't a word