Angela Schwenk-Schellschmidt (BHT Berlin): The Common Idea behind all Roulettes, one Formulae Fits for All - an Application of Complex Numbers |
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Csütörtök, 4. Szeptember 2014, 15:00 - 16:00
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Abstract. A roulette is the curve traced out by a point that is attached to a curve (wheel) as the curve rolls along another curve (street) without slippage. Mostly the wheels are circles and the streets are straight lines or other circles. Normally the parameterisation of a roulette is derived by a special solution
that fits only for the considered type of wheel and street. Changing the type of the wheel or the type of the street requires new thinking just form the beginning. But there is one common idea behind all roulettes. This idea fits to all situations. One just needs a time depending Euclidean motion that transforms the wheel from its starting position to its current position. A general formula is derived. Just by plugging in the equations of the wheel and the street generates the equations of the roulette or the current equation of the rolling wheel. Complex numbers make the formula very simple. |
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Hely : Bolyai Intézet, Irinyi udvari terem |
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