101 uses of a quadratic equation Chris Budd

101 uses of a quadratic equation Chris Budd

Is the quadratic equation evil? And does anyone care?

Babylonians Counted in Base 60

x Area x x

Quadratic equation Solutions

X = 1. 4142135623730950488… A 4 Paper

Conic sections Appolonius Cone

Ellipse

Parabola

Hyperbola

Ellipse Parabola Hyperbola All these curves obey quadratic equations

How conic sections caused a revolution

Copernicus

Tycho Brahe Kepler

Galileo Studied how things move and found that they obeyed quadratic equations

Cars do …. . THUD!! . . Was the car speeding? Forensic evidence: collision damage, witness statements, skid marks

s u F distance of skid speed brake force Quadratic equation links them together Solving the equation gives the speed

So do rugby balls …. Parabola

Sir Isaac Newton Explained the link and also invented the reflecting telescope based on the parabola

Newton discovered differential equations Used to explain almost everything • Pendulums • Car suspensions • Musical instruments • Radios and TV

Euler finds the solution Solve the quadratic equation to solve the differential equation And millions of important problems

Quadratic equations take flight Speed Pressure Bernouilli

Chaotic quadratic equations Bee population x evolves every year

population a=2 Population settles down

population a=3 Boom and bust

population a=4 Chaos

Are you still frightened of me?