Inside this regular octagon sit two squares of area 8. What’s the area of the shaded rectangle?pic.twitter.com/FgdfcoY1aj
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Inside this regular octagon sit two squares of area 8. What’s the area of the shaded rectangle?pic.twitter.com/FgdfcoY1aj
I think a dissection argument is simplest, and perhaps also the most elegant.pic.twitter.com/fbABrw2jzC
That's beautiful!
And how about these amber parts?
cc @mathhombrepic.twitter.com/wweOoVqsx3
I really like the way these A-size rectangles and half-squares can tile together. Lots of interesting things to see. What size regular octagons can we make?pic.twitter.com/Esi7y1YSHb
If the short side of the half-square is 1, then by repeated substitution you can achieve regular octagons with side lengths A * B^n for any n>= 0 (where A = sqrt(2) and B = 1+sqrt(2) ). Looks like it'll lead to an octagonal version of this: https://en.wikipedia.org/wiki/Pinwheel_tiling … !pic.twitter.com/Q9baSAVSzq
That's nice (and thanks for the link)! Those aren't the only sizes of regular octagons I can get though...
Oh yeah, there's also simple doubling of the two basic units as well (which multiplies sidelength by A=sqrt(2)), so the formula above becomes A^m*B^n (with n >=0, m >= 1)... any others you know of?pic.twitter.com/sz9wMrj5wt
Whoops, looks like our tweets crossed!
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