Geometry and Arithmetic
Part of the Undergraduate Texts in Mathematics book series (UTM)
Everyone knows what a rational number is, a quotient of two integers. We call a point in the (x, y) plane a rational point if both its coordinates are rational numbers. We call a line a rational line if the equation of the line can be written with rational numbers; that is, if its equation is
with a, b, c,rational. Now it is pretty obvious that if you have two rational points, the line through them is a rational line. And it is neither hard to guess nor hard to prove that if you have two rational lines, then the point where they intersect is a rational point. If you have two linear equations with rational numbers as coefficients and you solve them, you get rational numbers as answers.
$$ax + by + c = 0$$
KeywordsSine Fermat sinO
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© Springer Science+Business Media New York 1992