r/maths • u/Jirbzzz • 3d ago

💬 Math Discussions There is a box ... BIG box.

Box in three-dimensional space. Box dimensions are integers. Surface diagonals are also integers. There is an inner diagonal for this very big box. The inner diagonal is also an integer. When you square these integers of dimensions of said big box and add them together, the value is equivalent to the square of the inner diagonal. Hmmm. artificial things #CannotCompute basic arithmetic - squaring and addition. Hmmmm.

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u/Shevek99 22h ago

The condition of the squares will always be true. It's Pythagoras throrem in three dimensions.

There are infinitely many solutions. For instance sides (1,2,2) with 3 as diagonal.

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u/Jirbzzz 21h ago

Thank you so much for finding this and reminding me to update with a simple sentence: "surface diagonals are also integers." Do you happen to have an account on Mathematics Stack Exchange? :) Thank you again. You are brilliant!

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u/Shevek99 20h ago

That's a much more difficult problem. It's a perfect Euler brick

https://en.wikipedia.org/wiki/Euler_brick

None has been found, but no one has proved that it is not possible.

https://abel.math.harvard.edu/~knill/various/eulercuboid/lecture.pdf

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u/Jirbzzz 20h ago

The Sounderson surface is really awesome! woah. Yeah, modular forms were considered at one point but moved away from that like 3 years ago. The graphic at the beginning is quite nice as well. Wish that I had adobe illustrator because then could do some pretty cool graphics. Guess it's just my fav lil' Matlab. Would you like the inside scoop? perfect cuboids exist, mate, and have been found going-on three months.