We consider a simple problem in probability: A thin rod is broken at random into three pieces. What is the probability that these three pieces can be used to form a triangle? This problem is solved without difficulty. If the rod is of unit length, aligned along the interval $latex {0\le x \le 1}&fg=000000$, we…

ThatsMaths

21.03.2024

The Many Schools of Mathematical Thought – ThatsMaths

Mathematics is used widely, playing a central role in science and engineering and, increasingly, in the social and biological sciences. But users seldom consider the fundamental nature of mathematics. Many cannot improve on the vacuous definition: mathematics is what is done by mathematicians. We could try harder, with something like “mathematics is the language of…

ThatsMaths

04.04.2024

Pythagorean Tuning and the Spiral of Theodorus – ThatsMaths

Most of us are familiar with the piano keyboard. There are twelve distinct notes in each octave, or thirteen if we include the note completing the chromatic scale. The illustration above shows a complete scale from middle C (or C$latex {_4}&fg=000000$) to the C above (or C$latex {_5}&fg=000000$). Eight of the notes --- C, D,…

ThatsMaths

18.04.2024

Resonant Vibrations from Atoms to the Far Horizons of the Cosmos – ThatsMaths

Panta Rhei — everything flows — said Heraclites, describing the impermanence of the world. He might well have said “everything vibrates”. From sub-atomic particles to the farthest reaches of the cosmos we find oscillations. Vibration is key for aircraft wing, motor engine and optical system design. Ocean tides forced by the Moon and seasonal variations…

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Breaking a Stick to Form a Triangle – ThatsMaths

The Many Schools of Mathematical Thought – ThatsMaths

Pythagorean Tuning and the Spiral of Theodorus – ThatsMaths

Resonant Vibrations from Atoms to the Far Horizons of the Cosmos – ThatsMaths

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