Are there any Complex number formulas used in sundial calculations?
To all the maths people out there, My background is not math, and I don't know how to do the math to approach this question. I do know that complex numbers are used in engineering for work with alternating current and frequency samples in electrical signals. Since sundials deal with cycles, are there any sundial relationships that use complex numbers? Any starting point would be appreciated. Thanks, Warren Thom --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: Are there any Complex number formulas used in sundial calculations?
Hi Warren, There are many ways to express and solve the geometric relationships encountered in sundialing. In earlier times, geometric methods, such as nomograms and dialling scales, were developed. One, presented by Fred Sawyer at a BSS Conference some years ago and published in the NASS Compendium, solves the commonest equation: tan(A)/tan(B)=sin(C). Repeated application of this equation solves the majority of sundial problems. When tabulated trig functions became available, and since calculators became affordable, trigonometric equations involving only real (not complex) scalars (i.e. numbers, not vectors) became the favoured form. Tony Belk recently published a series of articles in the BSS Bulletin on vector methods, which seem to solve certain problems very well. Others, myself included, like the elegance of matrices. But neither vectors (which are one-dimensional matrices) nor two-dimensional matrices are well supported by the commonest computer languages (who, I wonder, has an APL interpreter?), so we stick to what we know and can persuade a computer to calculate, which is scalars. As far as I can think, complex numbers haven't featured. As spherical geometry involves three dimensions, complex numbers, which only have two, would seem to be rather limited. Quaternions are, if you will, four-dimensional complex numbers, so could, I suppose, be used. Doubtless someone with greater mathematical knowledge than I will correct me if I am wrong, but I think it is safe to say that complex numbers aren't used by the huge majority of us, if, indeed, they are used at all. Regards Chris Complex numbers are tools. - Original Message - From: Warren Thom [EMAIL PROTECTED] To: Sundial List sundial@rrz.uni-koeln.de Sent: Tuesday, October 17, 2006 12:30 PM Subject: Are there any Complex number formulas used in sundial calculations? To all the maths people out there, My background is not math, and I don't know how to do the math to approach this question. I do know that complex numbers are used in engineering for work with alternating current and frequency samples in electrical signals. Since sundials deal with cycles, are there any sundial relationships that use complex numbers? Any starting point would be appreciated. Thanks, Warren Thom --- https://lists.uni-koeln.de/mailman/listinfo/sundial --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: Are there any Complex number formulas used in sundial calculations?
Chris Lusby Taylor wrote: When tabulated trig functions became available, and since calculators became affordable, trigonometric equations involving only real (not complex) scalars (i.e. numbers, not vectors) became the favoured form. Tony Belk recently published a series of articles in the BSS Bulletin on vector methods, which seem to solve certain problems very well. Others, myself included, like the elegance of matrices. But neither vectors (which are one-dimensional matrices) nor two-dimensional matrices are well supported by the commonest computer languages (who, I wonder, has an APL interpreter?), so we stick to what we know and can persuade a computer to calculate, which is scalars. Well put, Chris... I imagine plane trigonometric functions (and, by extension, spherical) can be expressed in complex form, but it's not necessary or particularly a better way of doing things. As for vector and matrix math(s), I agree not many have access to APL, and few can justify Matlab for home use, but take a look at Euler some time. Completely free, long history, (since 1988.), supported under Windows, Linux, and even an old OS/2 version. Far smaller than Matlab, too - around 67 MB. http://mathsrv.ku-eichstaett.de/MGF/homes/grothmann/euler/ Dave --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: Are there any Complex number formulas used in sundial calculations?
At 15:56 17-10-2006, Dave Bell wrote: Chris Lusby Taylor wrote: When tabulated trig functions became available, and since calculators became affordable, trigonometric equations involving only real (not complex) scalars (i.e. numbers, not vectors) became the favoured form. Tony Belk recently published a series of articles in the BSS Bulletin on vector methods, which seem to solve certain problems very well. Others, myself included, like the elegance of matrices. But neither vectors (which are one-dimensional matrices) nor two-dimensional matrices are well supported by the commonest computer languages (who, I wonder, has an APL interpreter?), so we stick to what we know and can persuade a computer to calculate, which is scalars. Well put, Chris... I imagine plane trigonometric functions (and, by extension, spherical) can be expressed in complex form, but it's not necessary or particularly a better way of doing things. As for vector and matrix math(s), I agree not many have access to APL, and few can justify Matlab for home use, but take a look at Euler some time. Completely free, long history, (since 1988.), supported under Windows, Linux, and even an old OS/2 version. Far smaller than Matlab, too - around 67 MB. http://mathsrv.ku-eichstaett.de/MGF/homes/grothmann/euler/ Dave or have look at Scilab at: http://www.scilab.org/ (it is free) Scilab has even a Matlab to Scilab conversion tool. Thiabud Chabot Th. Taudin Chabot, . [EMAIL PROTECTED] --- https://lists.uni-koeln.de/mailman/listinfo/sundial
