Mathematics students have cause to celebrate. A University of New South Wales academic, Dr Norman Wildberger, has rewritten the arcane rules of trigonometry and eliminated sines, cosines and tangents from the trigonometric toolkit. What's more, his simple new framework means calculations can be done without trigonometric tables or calculators, yet often with greater accuracy. Established by the ancient Greeks and Romans, trigonometry is used in surveying, navigation, engineering, construction and the sciences to calculate the relationships between the sides and vertices of triangles. "Generations of students have struggled with classical trigonometry because the framework is wrong," says Wildberger, whose book...