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1). TRIGONOMETRIC FUNCTIONS CAN BE EXPRESSED AS ROOTS OF POLYNOMIALS. As any fule kno; “The squaw on the hippopotamus is equal to the sons of the squaws on the other two hides”. What Pythagoras may not have realized though, is that his famous theorum solves just the first subset of an interesting series of equations. Read the online version or download the Word 6 version (45k) with Excel demonstration spreadsheets. These graphs look a bit like quantum wave packets to me, if it could be proved that the sum of the discarded terms is zero. 2). DRAW A PENTAGON WITH JUST A STRAIGHT EDGE AND A COMPASS. The solution to the equations in section 1 for the angles of a pentagon proves the relationship between their trigonometric functions and the square root of 5. This enables the accurate construction of a regular pentagon, and here is one way to do it. Try the Pythagoras homepage for more on the Golden Mean (and a lot of mystical stuff). 3). WHY ARE THERE TWELVE SEMITONES IN AN OCTAVE? The difference between ‘Justly Intoned’ and ‘Equally Tempered’ musical scales is explored in Tuning for Sound, where there is also a new and not very mathematical section on ocarinas. 4). ELECTROMAGNETIC EQUATIONS AS CROSS PRODUCT VECTOR MULTIPLICATIONS. It is possible to express the general electromagnetic equations as a vector cross product. This is either:- F = q d/dt Bl or F = q d/dt lB where F = force q = charge B = magnetic field l = length t = time. It has been a long time since I wrestled with Fleming’s Left Hand Rule, so I cannot say for sure which of these equations is actually correct. If anyone could enlighten me with an elegant explanation, I can put your link here.

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