Pentagon from Rectangle Tutorial

For all those times when you woke up in the middle of night and said to yourself, "What I really need right now is a pentagon, freshly cut from some copy paper."
Visit my channel here for more tutorials: / samsorigamidojo

[@flatlanding]

excellent job, very smart to use the rectangle instead of cutting out a square...

[@rlwemm]

After some scientific experimentation (ha ha-trial and error), I discovered that the ratio is 1.41 - same as A4. So, take the short side and multiply it by 1.41 to get the best pentagon. Shorter lengths will result in a corner slightly cut off, which makes folding difficult.

[@rlwemm]

@Jesse Lucas And proud of it!

[@jessevanderduin]

The geometry of the folds show that this method gives a perfect pentagon for a ratio of: 4×sin(π/5)/(1 + cos(π/5)) = 4 sqrt(1 - 2/sqrt(5)) = 1.2996... Thus a ratio of approximately 1:1.30, which is incredibly close to the ratio of US letter paper, which is probably why this method works so well. I have also tried to fold the pentagon with A4 paper, but don't get nearly as good a result as with US letter paper. Having said that, the thickness of the paper of course also greatly affects the precision of the pentagon, so even though mathematically the ratio 1:1.30 should give a perfect pentagon the actual result may differ depending on the thickness of the paper used. Maybe that's what gave your different result?

[@lizardmccroc]

Thank you, Sam. :)

[@mckmck6220]

Tq I tried many videos but it was not come clear pentagon but by u r video it came perfect tq very much brother

[@maryb.4559]

thank you!

[@adityaverma8800]

You are a great I make a pantogon rose But I do not cut a pantogon And yo find my problem therefore Yo are a great man

[@marvinhenrie8966]

Nice job kid, thanks

[@rlwemm]

It does not work for every rectangle. I think the ratio is 1:1.3333 but I'm not sure.