Re: 475 questions


ciclista41@...
 

Hi Albert,

Yup, 2.22 is ~ pi/√ 2! And I did not know that, but I thought the consistancy of the ratios between those measurements on each rail might indicate something to somebody, and you were the one! Very interesting observation.

My trigonometry is rusty, but maybe I'll look into the math behind this more deeply when I don't have such a steep learning curve going, anyway. My guess is that this has something to do with the sine wave and the fact that pi is derived from the circumference of a circle and 1/√ 2 is the sine of the unit circle at 45° (1/(4pi) radians). Since the sine wave is what we use to describe the oscillation of voltage with respect to time in AC and is also the graph of the values of the sine of an angle as it goes through the 360° (2pi radians) of a full circle (1 Hz), it has to make sense there, somewhere! My calculus is incalculably rustier than my trigonometry, given that I never had the opportunity to teach calculus in my entire career, but it could also derive from the derivative of the sine function. ;-)

Bruce

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