The ratio for 3 thirds is simply 1/2, the 2 being the 2 thirds, and the 1 being the rest.
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The ratio is 57 cubed. This answer does not depend on the fact that you are comparing two similar pyramids; it works the same for two cubes, two spheres, etc. - in general, for any two similar 3D objects.
The ratio is the same as the ratio between the number of teeth.
The golden ratio, or golden mean, or phi, is about 1.618033989. The golden ratio is the ratio of two quantities such that the ratio of the sum to the larger is the same as the ratio of the larger to the smaller. If the two quantities are a and b, their ratio is golden if a > b and (a+b)/a = a/b. This ratio is known as phi, with a value of about 1.618033989. Exactly, the ratio is (1 + square root(5))/2.
Yes. But if you have a ratio of two integers, the ratio will be rational by definition.
One third divided by two and one third = 1/7