Daily Maths Challenges

216 readers

3 users here now

Share your cool maths problems.

Complete a challenge:

Post your solution in comments, if it is exactly the same as OP's solution, let us know.
Have fun.

Post a challenge:

Doesn't have to be original, as long as it is not a duplicate.
Challenges not riddles, if the post is longer than 3 paragraphs, reconsider yourself.
Optionally include solution in comments, let it be clear this is not a homework help forums.
Tag [unsolved] if you don't have a solution yet.
Please include images, if your question includes complex symbols, attach a render of the maths.

Feel free to contribute to a series by DMing the OP, or start your own challenge series.

founded 10 months ago

MODERATORS

siriusmart

[solved] A tale of two rabbits (self.dailymaths)

submitted 1 week ago* (last edited 1 day ago) by joelthelion to c/dailymaths

12 comments fedilink hide all child comments

I have ten meters of mesh fence. I want to make two enclosures for my rabbits who can't stand each other (they can share a wall). What is the shape and the area of the largest enclosure (in terms of area) I can build? Each rabbit needs to have access to the same area. The shape can be arbitrary (although it would be nice if it were continuous or smooth to some extent, and each area contiguous).

Examples:

A square of 2x2m, divided by a 2m wall. Area: 4 square meters

A circle of radius 1.21m, divided by a wall. Area: ~4.58 square meters.

Is it possible to do better?

you are viewing a single comment's thread
view the rest of the comments

[–] A_A 3 points 1 week ago* (last edited 1 week ago) (2 children)

i have the same result, glad for your rabbits (and for you) !
P.S. : You can change the flare to [solved]

[–] joelthelion 2 points 1 day ago* (last edited 1 day ago)

I've implemented a gradient descent algorithm in python to optimize the shape, and I get essentially the same thing:

I'm changing the title to solved :)

Here's the code: https://pastebin.com/wKvhVvQg

[–] joelthelion 1 points 1 week ago

You have the best solution so far, but I wouldn't call it solved yet, since we don't have any proof or indication that it is the best solution that exists.