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How did you know to adjust the values of the resistors and capacitors, in order to use a 3 V supply instead of the 9 V supply he used? Trial and error, or did you work through equations to find the values?
I read over the article but it doesn't go over the mathematical derivations for how the selection of resistor and capacitor values affect the on/off time of the 555 timer or how he selected the values of the inductor/capacitor of the flyback converter.