*all*of them:

### Click Here For a Lot of Numbers

At the start, Wolfram Mathematica was being a little obtuse with me, but then I switched to Python, and it turned out just fine. Here is the Python file for those of you who are interested.

You guessed it! But how many do you think you can actually find? I bet you 13228 moneyz in geometric currency that you can't beat my supercomputer. I dare you to check *all* of them:

###
Click Here For a Lot of Numbers

At the start, Wolfram Mathematica was being a little obtuse with me, but then I switched to Python, and it turned out just fine. Here is the Python file for those of you who are interested.

Just kidding, I don't have a knock knock joke. But I do have a fascinating mathematical exploration to tell you about! After figuring out how to identify the acuteness of a triangle with only knowing side lengths in class (shoutout to Vikram for helping me/telling me what the answer was), I decided to write a little program to do these calculations.

Its nice. It does nice things. But I'm starting to worry about its accuracy. Here is the algorithm I am using:

Right triangle (never happens because I use random coordinate inputs that are decimals):

A^2 + B^2 = C^2

Acute:

A^2 + B^2 < C^2

Obtuse:

A^2 + B^2 > C^2

Also note that these are all real triangles, no floppy arm business like this: https://docs.google.com/drawings/d/1vqFSweJkqJm-2oSSe6q3nbhRDJ4l1LDcGIFDeid5STQ/edit

The thing that perplexed me was that there seemed to be A LOT more acute triangles than obtuse. I've been running this program with random triangles (in a finite 500 by 500 space) 200 times a second for over 10 minutes and the obtuse to acute ratio seems to be wavering around 1:2.645. Why? Is it a problem with my program, or a problem with...MATH?

Update: Whoops, I think I got my alligator teeth mixed up again! Its 2.645:1 which makes a bit more sense.

Another update: As you change the dimensions of the rectangle you are generating the triangles in the ratio changes. What is the correlation between the dimensions of the rectangle and the acute/obtuse ratio?

Its nice. It does nice things. But I'm starting to worry about its accuracy. Here is the algorithm I am using:

Right triangle (never happens because I use random coordinate inputs that are decimals):

A^2 + B^2 = C^2

Acute:

A^2 + B^2 < C^2

Obtuse:

A^2 + B^2 > C^2

Also note that these are all real triangles, no floppy arm business like this: https://docs.google.com/drawings/d/1vqFSweJkqJm-2oSSe6q3nbhRDJ4l1LDcGIFDeid5STQ/edit

The thing that perplexed me was that there seemed to be A LOT more acute triangles than obtuse. I've been running this program with random triangles (in a finite 500 by 500 space) 200 times a second for over 10 minutes and the obtuse to acute ratio seems to be wavering around 1:2.645. Why? Is it a problem with my program, or a problem with...MATH?

Update: Whoops, I think I got my alligator teeth mixed up again! Its 2.645:1 which makes a bit more sense.

Another update: As you change the dimensions of the rectangle you are generating the triangles in the ratio changes. What is the correlation between the dimensions of the rectangle and the acute/obtuse ratio?

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