Math Puzzle [num18]

Cut at every 72 degree? Pretty much splitting the pizza into 5 equal parts and they should have equal crust amounts?

Like this except actually at every 72 degree angle.

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the corner (crust)will not be of equal area isnt it?

Split the perimeter into 5 equal chunks arbitratily (and none of the chunks are disjoint). Join the 5 boundary points towards the centre of the square with straight lines. The 5 resulting areas satisfy the criteria, since each chunk can be split up into at most 2 triangles, with base on the boundary and a height of 1/2. So each area is 1/2*1/2*4/5=1/5 as required.

The SQUARE pizza can be treated as a RECTANGULAR pizza with no crust on the left and right side and only crust on the top and bottom. Cut the slices vertically and it should be easy to make them even? Rectangle is fatter and shorter while the square is skinnier and taller making them even?

Oh hey this works for any number of pizza eaters, cool!

The corner counts twice, so the remaining ones do indeed have 8 perimeters.

In that case take a triangle out of each side of the pizza (long base edge along crust side) of base 4/5, height 1/2. (this is for square pizza side length 1, can scale to whatever side length). This results in 4 pieces of base (crust) 4/5 units each, leaving 4/5 units of crust for the remaining piece. Each of these pieces has area 1/5 square units, leaving 1/5 for the remaining piece.

*edit* hmm, remaining piece is cut by the others so this doesn't work :<, i guess it depends if you allow the pizza to be counted as one piece when connected by a single point

I like drawing 5 pointed stars so I could roughly get 5 points evenly split inside a square. You can then have a cut from the center point through each point or half way point (prefer half way for neatness!)

seems pretty simple which means i must be misunderstanding it
but here's what i got (based on the android game sliceit)
so for simplicity's sake let's say its a 5x5 pizza
divide border into 5 cuts, 4 squares long each
from there, make cuts such that each piece is 5 squares in area?


O-o
edit:
come to think of it, you can just cut straight to centre of pizza. should be pretty trivial to see why