Question

Relation of irrational numbers and geometrical constructions

Answer 1

Answer:

Rational Number is defined as the number which can be written in a ratio of two integers. An irrational number is a number which cannot be expressed in a ratio of two integers. In rational numbers, both numerator and denominator are whole numbers, where the denominator is not equal to zero.

I think that we agree a number like square root of 2 counts in geometry. We can construct it using the fundamental theorem of Pythagoras. If we hypothesize a coordinate system, we can place the square root of 2 on a line segment of appropriate length. Like one of length 2, from 0 to 2. We can place the rational numbers to approximate it from both directions.

It proceeds that any such irrational number constructible by Pythagorean triples can be placed on any line segment of sufficient length. The rational numbers to approximate it are points on this line segment.

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