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Define these Levels of Measurement.NominalOrdinalInterval/Ratio
-3 is the ratio of -3 to 1. It's also the ratio of 3 to -1, and the ratio of -12 to 4, etc. Any one of those facts proves that -3 is rational.
We will call the golden ratio, 1.618033989:1, G. G2-1=G; 1/G+1=G; (1+G)/G=G; For more, research golden ratio on wikipedia.
Equal intervals between points of that scale and a true zero
The ratio of the length of the side opposite a given angle to the hypotenuse is the sine of that angle.The ratio of the length of the side adjacent to a given angle to the hypotenuse is the cosine of that angle.The ratio of the length of the side opposite a given angle to the side adjacent to that angle is the tangent of that angle.