the ratio of ratio

Number Theory Level 2

Can golden ratio : silver ratio :bronze ratio ,written as the ratio p:q:r ,while (p,q,r) belongs to the positive integers field.If so what is it ? Hint : those ratio are called Metallic mean

Yes ,3:4:5 Yes ,1:2:3 No Yes ,2:3:4

ho Yin Li by ho Yin li , 21, Hong Kong

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1 solution

ho Yin Li
Sep 9, 2019

there are all irrational number consisting the term √5 ,√2,√13 respectively which is mutually irreducible .

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Maybe it is a good idea to include the ratios in the description of your problem, as I think people are not too familiar with the ratios (I only heard of it via youtube someday, which was just completely random). By the way, you might want to change your "About" on your profile as I think people won't really appreciate it...

Joël Ganesh - 1 year, 9 months ago

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i notice your concern ,i have changed my about .However in the question ,i intentionally not include the ratio just to give motivation for reader to check by themselves.

ho Yin li - 1 year, 9 months ago

This question really needs to be written in a more comprehensible fashion.
a) give some background about the three ratios.
b) "while (p,q,r) belongs to the positive integers field" Two issues: If the idea is to require all three of p,q, and r be integers, don't list them as a 3-tuple.
Also, the integers are not a field.

Richard Desper - 1 year, 9 months ago

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