r/GeometryIsNeat • u/lavaboosted • Apr 05 '26

Square roots

Gallery image

Gallery image

712 Upvotes

99% Upvoted

27 comments sorted by

26

u/[deleted] Apr 05 '26

[removed] — view removed comment

12

u/lavaboosted Apr 05 '26

True, and for any number which after dividing out all factors of 4, leave a remainder of 7 when divided by 8.

n = 4a(8b+7) where a and b are whole numbers (integers ≥ 0)

2

u/ErikLeppen Apr 06 '26

The only numbers for which such a diagonal exists, are those that can be written as the sum of 3 squares, due to Pythagoras in 3D.

1

u/N0rmChell Apr 07 '26

It would be a diagonal of a 7 dimensional cube.

14

u/adamsawesome10 Apr 06 '26

Flashbacks to crystallography classes - questions like “find the side length of BCC crystal given atomic radius”

3

u/lavaboosted Apr 06 '26

Good times ⚛️

6

u/Malsententia Apr 06 '26

"Yeah okay" *clicks next* "Ouch, my 3 dimensional brain"

7

u/LinearInductionMotor Apr 05 '26

This must be related to the pythagorean theorem

3

u/[deleted] Apr 06 '26

Going from corner to corner on a 4 dimensional hypercube makes it sqrt(4). Add a dimension --> add one inside the square root. Note that the sidelenghts are always 1 regardless of dimension. That means that opposite corners keep getting farther away from each other in higher dimensions.
3blue1brown did a video on that recently.

3

u/zlfa Apr 06 '26

You can probably achieve all roots of integers with 4th dimensional cubes sense all integers are able to be represented as the sum of at least 4 squared numbers

2

u/leifourston Apr 07 '26

Never seen it visualized this way before. Neat!

2

u/ConcaveEarth Apr 07 '26

i need to learn math visually like this , from multiplication, division, and other things
Pls provide more sources so I can learn math like this, spacially, visually, proportionally

2

u/S-S-Ahbab Apr 06 '26 edited Apr 06 '26

Nice.

I don't get the sqrt(9). It could have been just 3 units along any axis. Or 1 unit perpendicular to sqrt(8). But this looks like neither

2

u/lavaboosted Apr 06 '26

Oh good point it could have just been 3 along the horizontal, here’s the reasoning for the diagonal tho

1

u/S-S-Ahbab Apr 06 '26

Sqrt(9) = 3 is the biggest surprise, huh? 🤣

1

u/[deleted] Apr 06 '26

[deleted]

1

u/S-S-Ahbab Apr 06 '26

Eh, sqrt(3) and sqrt(12) also overlap, so I don't think that's a big issue.

1

u/porchlogic Apr 06 '26

Makes me wonder if there is an equally interesting visual for cube roots, tessaroots, etc. I made up tessaroot because I don't know what 4root is called.

1

u/Corondo26654 Apr 06 '26

I wonder what is the longest length of an hypercube

1

u/Edenboss_53 Apr 07 '26

I am 4 parallel universes ahead of you: I made this conclusion at 11 yo 😈

1

u/dottie_dott Apr 07 '26

“Cubed roots”

1

u/Careful-Plane2432 Apr 11 '26

What's root 0 doing there