Exploring maths through problem solving

Problem of the Week

Banana Rotation

After a few days, a banana becomes too ripe to eat. If this picture had perfect rotational symmetry, what is the order of rotation? Within what angle would you find the stems of the bananas you would eat?

Heather McMaster


Assuming the bananas are identical shapes rotated around a point in the centre of this arrangement, the angle between the middle of one banana stem and the next (or the place midway between one ‘in between’ space and the next) is 360° ÷ 15 = 24°.

In other words, if you rotated the image of banana shapes by 24°, it would look the same. The order of rotation of the image is 15.

The angle in which the bananas are acceptable for you to eat, is 24° for a pair of adjacent bananas and another 24° for each banana after that.

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