tag:blogger.com,1999:blog-5304409.post2451563990597678087..comments2020-07-05T12:37:28.179-07:00Comments on Amit's Thoughts: Dividing a range into segmentsAmithttp://www.blogger.com/profile/12159325271882018300noreply@blogger.comBlogger7125tag:blogger.com,1999:blog-5304409.post-55068468294014387672012-12-29T16:43:06.166-08:002012-12-29T16:43:06.166-08:00Also see Equidistribution TheoremAlso see <a href="http://en.wikipedia.org/wiki/Equidistribution_theorem" rel="nofollow">Equidistribution Theorem</a>Amithttps://www.blogger.com/profile/12159325271882018300noreply@blogger.comtag:blogger.com,1999:blog-5304409.post-6468022384470992152008-05-23T05:53:00.000-07:002008-05-23T05:53:00.000-07:00They're still uneven but it's unavoidable. This sc...They're still uneven but it's unavoidable. This scheme leaves them as even as possible (I think) given the constraint that they need to be roughly even after each division.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-5304409.post-41962905299722462242007-08-05T16:56:00.000-07:002007-08-05T16:56:00.000-07:00Thanks anonymous! Yes, using the fractional compon...Thanks anonymous! Yes, using the fractional component connects this problem to the cyclical nature of the golden angle. BTW, <A HREF="http://www.sciencenews.org/articles/20070505/mathtrek.asp" REL="nofollow">plants may not necessarily follow the golden ratio and Fibonacci sequence</A>.Amithttps://www.blogger.com/profile/12159325271882018300noreply@blogger.comtag:blogger.com,1999:blog-5304409.post-69503996176554367762007-08-03T05:26:00.000-07:002007-08-03T05:26:00.000-07:00This is a recasting of the familiar link between t...This is a recasting of the familiar link between the golden ratio and phyllotaxis; successive leaves are in a certain sense as far as possible from previous ones if they are separated by the previous one by an angle of 360°/(1+φ), about 137.5°.<BR/>See:<BR/>Stephen Wolfram, "A new kind of science" §8.6 at http://www.wolframscience.com/nksonline/toc.html<BR/>http://en.wikipedia.org/wiki/Golden_angle <BR/>http://en.wikipedia.org/wiki/Fermat%27s_spiralAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-5304409.post-24895545727020432502007-08-02T08:44:00.000-07:002007-08-02T08:44:00.000-07:00Amit,Just wanted to let you know that over the yea...Amit,<BR/><BR/>Just wanted to let you know that over the years I have found some of the material on your website really useful. I am a hobbyist game programmer(wannabe is more like it) but I really enjoy reading some of your articles on pathfinding etc.<BR/><BR/>BTW how is supreme commander:D Have to upgrade my system to handle the damn game.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-5304409.post-65181984663990295122007-07-31T16:04:00.000-07:002007-07-31T16:04:00.000-07:00Yes, you're right — I meant to take the fractional...Yes, you're right — I meant to take the fractional component of i * φ.<BR/><BR/>They're still uneven but it's unavoidable. This scheme leaves them as even as possible (I think) given the constraint that they need to be roughly even after each division.Amithttps://www.blogger.com/profile/12159325271882018300noreply@blogger.comtag:blogger.com,1999:blog-5304409.post-63610894230205624892007-07-31T16:01:00.000-07:002007-07-31T16:01:00.000-07:00The Golden Ratio (Phi) is greater than zero (1.6.....The Golden Ratio (Phi) is greater than zero (1.6...).<BR/><BR/>If the i th division is given by phi * i, would be greater than 1, wouldn't it? Where would that slice in your rescaled range of 0-1?<BR/><BR/>Also, this still leaves the problem of *uneven* slices.Alokhttps://www.blogger.com/profile/00541962357236077809noreply@blogger.com