In earlier times, Birthday cakes were mostly round in shape. Scholars associate religious beliefs and technical compulsions for the same. Greeks offered round shape cake to the Goddess of Moon – Artemis as it signified moon. They even placed candles on the cake to make the cake glow like the moon.
Some scholars opine that cake in the ancient world has association with the annual cycles. Round shapes of cakes were preferred as these represented the cyclical nature of life. Most specifically, the sun and moon.
Technical reason given for the roundness of the cake is that most cakes we know off advanced from the bread. In ancient times breads and cakes were made by hand. Typically, these were fashioned into round balls and baked on hearthstones or in low, shallow pans. Hence, these naturally relaxed into round shapes. With the progress of times baking pans of various shapes were developed and today we see cakes in imaginative shapes and sizes.

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