Radios used to depend on valves (tubes in the USA). When switched on these glass cylinders glowed bright red. To the left is a hysteresis curve. Such curves show graphically how valves behave when they are doing their job. I’m flirting with your boredom here, but bear with me.If you change the electrical values associated with the valve the shape of the curve changes. For me (an unwilling National Serviceman in the RAF) this was a half-opened window on how mathematics – so feared by liberal arts people (like me) – can not only describe the real world but to all intents and purposes is the real world.
Here’s a hint. The initial curve looks like part of a hill and – like a hill – has a gradient. Zoom in to a tiny part of the curve – so tiny it becomes a straight line. Incorporate that tiny line into a right-angled triangle. Does that light up a bulb? Pythagoras? Tall trees? Our long-lost friend trigonometry.
Fiddle with the values (angles, side lengths) of the triangle and the others change in an exact relationship. Simulating the effect of changing the electrical values associated with the valve. Using only paper and pencil (at least in those days – now we’d use a computer) we have designed an electrical circuit which will, for instance, help us amplify the tiny electrical signal picked up by the radio’s antenna so that it agitates a loudspeaker and we hear Messiaen’s Quartet for the End of Time. Or Amy Winehouse
