![]() Tessellations are frequently encountered in the art of M. ![]() This image was made using the Tess software mentioned below. A tree can quite easily be transformed into a shape that fills the plane without any gaps. This is one way of solving the problem with leftover dough shown in the top picture. Should you ever want to place circular cookies on a square baking sheet, this is how to maximize the size of the cookies! ( Illustrations CC-BY-SA by Toby Hudson) Oh yeah: a tessellation “is the process of creating a two-dimensional plane using the repetition of a geometric shape with no overlaps and no gap” according to Wikipedia. Using a square cookie cutter (or simply a knife) would be the easiest way to leave no gaps, but how cool are square cookies? What I’m really looking for are cookie tessellations which are aesthetically pleasing, and at the same time transferable to a baking sheet. ![]() To achieve this the cookies cannot be circular. My challenge for you however is a different one as I’m interested in eliminating the leftover dough when cutting cookies. The optimum way of placing 2-17 circles in a square are shown below (and the solution for up to 10.000 circles is also available). Many will perhaps start with a square packing (see below), but soon figure out that a hexagonal packing will fit even more cookies onto the rolled out dough or onto the baking sheet (especially when the dough/sheet is large compared to the cookies). The purpose is to maximize the distance between the cookies and maximize the size of the cookies, paying attention that the cookies should not touch. When cutting cookies from a rolled out dough or placing cookies on a sheet for baking you actually attempt to solve a mathematical problem known as a packing problem. More precisely I will delve into geometrical problems encountered in baking. For once I will leave the chemistry aside for a while and turn to the mathematical aspects of baking. ![]() It should come as no surprise that food, chemistry and mathematics meet in baking. Is there a way to avoid all that extra dough in between the cookies? (Photo: Christmas Tree Cookie Cutter from Bigstock) ![]()
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