Hexnet Hexagonal Tag Feed: trigonometry A feed of tagged nodes. https://hexnet.org/blog The way of the tau <p><a href="http://hexnet.org/content/dozenal-tau-unit-circle"><img src='/files/images/hexnet/tau-circle.png' title='Dozenal tau unit circle' alt='Dozenal tau unit circle' class='image-right'/></a> An astute reader recently brought to my attention the nascent movement afoot to replace &pi; in common usage with the number now unfortunately known as 2&pi;&mdash;viz., 6;349419 (dec. 6.283186): </p> <ul> <li><a class="ex" href="http://www.math.utah.edu/~palais/pi">Pi Is Wrong!</a> - By Bob Palais</li> <li><a class="ex" href="http://tauday.com/">The Tau Manifesto</a> - By Michael Hartl</li> </ul> <p> (For a reasonably convincing argument on why the letter &tau; (tau) in particular should be adopted for this value, please read Mr. Hartl's manifesto.) </p> <p> The fundamental point here is that, in trigonometry and all other manner of angle-measuring endeavors, what we care about is the radius of a circle, not its diameter. The one follows from the other to be sure, but at the end of the day the diameter is more usefully considered twice the radius than the radius is half the diameter. A circle is a circumference around a center&mdash;it is the measure of this distance between center and circumference that is elemental to the idea of a circle, not the rather incidental fact that its full width is twice that same distance. </p> Mon, 26 Jul 2010 03:28:45 +0000 https://hexnet.org/content/way-tau https://hexnet.org/content/way-tau Dozenal tau unit circle <p> This is a unit circle diagram using both dozenal notation (as with elsewhere on this site, using "A" and "B" for ten and eleven) and the newly proposed circle constant &tau; (tau), which is equal to 2&pi;. The advantages of &tau; over &pi; are numerous and obvious&mdash;instead of a full circle of arc being two of anything, it is just one &tau;. Put another way, &tau; is simply the number of radians in a circle. </p> Sun, 25 Jul 2010 00:47:33 +0000 https://hexnet.org/content/dozenal-tau-unit-circle https://hexnet.org/content/dozenal-tau-unit-circle An Introduction to Hexagonal Geometry <p><img src='/files/images/hexnet/p-6.png' title='Simple hexagon' alt='Simple hexagon' class='image-right'/> The following is a brief survey of some elemental properties of hexagons, and why they might be useful. It is not intended to be a comprehensive treatment of the subject. My specific concern here is with the mathematical properties of hexagons, and, to an extent, their role in the natural world. I have avoided discussing hexagons as they pertain to human culture, religion, history, and other "local" concerns, though there are many fascinating instances of hexagonality and sixness in these areas, and they will no doubt be treated more fully elsewhere at another time. </p> Fri, 16 Apr 2010 22:03:55 +0000 https://hexnet.org/content/hexagonal-geometry https://hexnet.org/content/hexagonal-geometry