# 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? :) – Mark N May 27 '15 at 13:02
• But how can you be sure? You just 'guess' something? – Mathias711 May 27 '15 at 13:47
• So cutting into sevenths by eye in the traditional way would be a equally valid answer? – Bob May 27 '15 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. – starsplusplus May 27 '15 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. – dennisdeems May 27 '15 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 :) – user2408578 May 27 '15 at 13:14
• @user2408578 But what about the crust/icing. The top/bottom slice will get almost all of it!! – Mark N May 27 '15 at 13:18
• How do you plan to measure the height of each slice? – Luke May 27 '15 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.

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? – Rand al'Thor Oct 21 '18 at 7:49