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Guests would then scramble for the crumbs, which were thought to bring good luck. The tradition has evolved to smashing cake in your significant other's face and is just about fun and silliness rather than luck. By Kristi Kellogg.
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What is the shortest length cut you make to do this? Of course it is possible to bisect a cake by slicing it through the middle, but that's too easy. Also, if the cake happened to have icing on the top, then cutting through the middle would result in one piece having all the icing, and one none. That's not fair! We're also going to add the restriction that we're not allowed to move pieces between cuts. The length of this cut will be the diameter of the cake. If we normalize our cake to say it has a radius of one unit, then the cut is two units in length. This would create a new circular cake with half the volume, and an annulus cake donut shape with the other half.
Fancy, but not efficient, and messy to cut.
55 Wedding Cake Cutting Songs | Brides
Things get a little more interesting if we want to cut the cake in half again. At one end of the spectrum we can slice it in half using a cut along the radius shown left below. At the other end of the spectrum we can lop off a segment from the edge shown below right , using a cut direction perpendicular to the radius cut.
There are an infinite number of solutions inbetween with the cut being at an arbitrary angle.
Interestingly, these are well-used formulas, as they have applications for things such as determining the volume of fluid in a circular tank laid on its side. They can also be used to determine the shape of a circular segmented transom window over a doorway if an architect knows the width of the top of the doorway, and the height she wants to make the window, then the related formula below can be used to determine the radius of the circle that meets these two criteria.
The height of the segment is given a fancy name of sagitta , and if you read my previous article on Vestigial Trig Functions you might appreciate that the sagitta is the Versin of half the angle of the sector. As the redius cut is length one unit, and the segment cut is 1.