Back to basics

Distance and angle are two basic terms in mathematics. What would happen if they were replaced by other terms? It is a refreshing question asked by N J Wildberger this fall.

For separation of points, quadrance is defined as the distance squared. Easy enough. It eliminates a few square-root signs. Pythagoras' is simply a + b = c when a, b , and c are the quadrances of the sides in a right-angled triangle.

For separation of lines, spread is defined as the square of the sine of the acute angle between the lines.

From these definitions he demonstrates the triple quad formula, the spread law, the cross law, and the triple spread formula. With these you are armed to solve most basic trigonometry questions.

Download the first chapter of his soon to be published book here. This is his home page.

Wildberger's fresh ideas is an excellent playground where you can set your students free to develop some math on their own.

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