# Cutting circular pie into seven equal parts

your task is to cut this pie (shown below) into seven equal parts.

What equal means by is size and shape
you have only one knife of length equal to cakes diameter and a scale to measure W and D but nothing else

Edit : Also there should be nothing of cake that that is wasted/eaten

• Can't we just cut it into 8 and eat 1? :) May 27, 2015 at 13:02
• But how can you be sure? You just 'guess' something? May 27, 2015 at 13:47
• So cutting into sevenths by eye in the traditional way would be a equally valid answer?
– Bob
May 27, 2015 at 14:07
• @Bob I +1ed your comment because this is a vague and overly broad question, but I think the idea is that you have a ruler but not a protractor. So, say W is 7cm, then you can make horizontal incisions at 1, 2, 3, 4, 5 and 6 cm heights using your ruler. But in order to cut slices of the right angle you would need something to help you measure 51.4°, and you don't have anything to do that with. May 27, 2015 at 15:57
• It's gonna be much much easier to cut 7 conventional slices just using the eye to judge the angle, than it is to make 7 perfectly level horizontal slices through the whole cake. May 27, 2015 at 18:03

Silly solution:

You cut through the Height? (the W in the picture). So you end up with 7 slices with the same diameter as the whole cake, but just 1/7th of its height.

• +1 Answers are not silly....rather the way we think are :) May 27, 2015 at 13:14
• @user2408578 But what about the crust/icing. The top/bottom slice will get almost all of it!! May 27, 2015 at 13:18
• How do you plan to measure the height of each slice?
– Luke
May 27, 2015 at 13:55

It's not possible to cut a circle into 7 pieces using geometric methods: Is it possible to divide a circle into 7 equial pizza slices..., unless you allow Neusis construction; see Heptagon for details on constructing a Heptagon, which can be overlaid on the pie and used to guide the slicing.

The only good solution that avoids geometry is the height-based slicing, as suggested by Anon.

Place a quarter in the center of the pizza.
Arrange seven dimes around the quarter.
Insert seven toothpicks in the “V” between the dimes.
Use the tooth picks as a guide to slice the pizza to the perimeter.
All seven eaters may enjoy equal slices.

Here is my solution.

You find the midway point of the radius of the cake. From there you would take a straight line across it from one side of the circle to the other. Then measure the distance from that midway point to the edge of the cake on this cross-section. Divide that in half. You now have the length you mark for the edge of each slice. Start at a point and measure out the length you got and make a mark. Do this until you have all seven slices.

Eight easy steps:

1. Make incision marks around the perimeter as for it being cut into 8.
2. Then take one of the 8th pieces, and guessage it into 7 divisions.
3. Then cut the first slice according to a Sixth+theSeventhOfTheSixth.
4. Once cut down both sides to the centre, take it and lay it on top of the next slice you want to cut.
5. Make a deep cut.
6. Rinse and repeat until you've marked out the whole circle.
7. Cut into seven.
8. Send me money.
• "guessage" seems a bit imprecise? Oct 21, 2018 at 7:49