Gear Ratios

In auto mechanics, gears and ratios are everywhere, and math is the only way to figure them out. Everything from ring and pinion ratios to transmission gear ratios and even tire sizes come into play for the final drive ratio. Some fourwheeldrive models have gearreduction axles, which allows major torque multiplication at crawl speeds, as well. These ratios are what determine what the speedometer says at any given speed. If even one of the gearing components is changed to a different size, the speedometer will read too fast or too slow.
Volume

Math is used to determine the size of each cylinder, and each of those is added up to a total, which is the displacement of the engine itself. Combustion chamber sizes must be known and calculated, as well as oil pan capacity and the cooling system capacity. Each of these components is dialed in using math in conjunction with special tools.
Tolerances and PSI

Every tolerance inside an engine requires math in order to work correctly. Cam and crankshaft endplay are dialed in using special gauges, as is the lash on the valves inside the heads. Each piston is designed using mathematical formulas so that when the rings are installed, a tight clean fit will be the result. The oil pump must operate at a certain pressure for each engine, which is figured out using math. Fuel delivery systems such as fuel injection require mathematical precision in order to maintain the correct pressure and flow throughout the rpm (revolutions per minute) range. Even the tires on the vehicle are inflated to a certain PSI, which is a mathematical equation in itself.
Other Numbers

Auto mechanics and engineers must also take engine rpm into account when designing or installing components. For instance, an engine idling at 600 rpm will need X amount of fuel and oil and coolant, whereas an engine racing along at 3,000 rpm will need much more, but still a specific amount. Belt lengths and sizes on the engine are all arrived at using math, as are hose thickness and lengths. The water pump must flow a certain amount for each rpm, and the radiator must have a capacity that matches the needs of the engine throughout different weathers and loadsall these answers are reached using math.