suppose you have a golden rectangle cut out of a piece of paper. now suppose you fold it in half along its base and then in half along its width. you have just created a new, smaller rectangle. is that rectangle a golden rectangle?

Question

12-05-2023
Mathematics

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suppose you have a golden rectangle cut out of a piece of paper. now suppose you fold it in half along its base and then in half along its width. you have just created a new, smaller rectangle. is that rectangle a golden rectangle?

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sqdancefan sqdancefan · Answer 1 · 2023-05-12T22:53:30+02:00

Answer:

yes

Step-by-step explanation:

You dilate a golden rectangle by a factor of 1/2, and you want to know if the result is a golden rectangle.

Dilation

Multiplying dimensions by a constant creates a similar figure, one with all the same dimension ratios as the original.

Golden rectangle

A "golden rectangle" is one that has an aspect ratio of Φ = (1+√5)/2 ≈ 1.618. Reducing its dimensions horizontally and vertically by a factor of 1/2 does not change that aspect ratio. It is still a golden rectangle.

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