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

[–] joelthelion 1 points 3 days ago

Here's another solution, that is suboptimal but might be preferable to the soap bubble solution in practice: an ellipse with long axis 1.592 and short axis 0.972. This should be close to the optimal ellipse (I used Kepler's approximate P=pi * (a+b) formula for the perimeter). It gives an area of 4.861 which is close enough to the current optimum, and looks like this: