Parabola developing as an envelope of lines in a triangle.
Reblogged from My Life, And Other Things That Suck
The Math Kid
A collection of mathematical fascinations, not strictly limited to the subject itself but also people's interactions and interpretations. My curiosity for the subject is infinite, but I try to stay away from the sciences. The thrill lies in the purity, not the application.
Info on my icon can be found here.
A beam detector for the unit circle is a set of points that intercepts any line crossing that circle, including tangents. It need not be connected. Obviously the circle itself provides an upper bound for the length required, at 2π. With some clever adjustments, however, this can be reduced significantly. The minimum required length is unknown, but the best known solution is given here. The length of this beam detector is approximately 4.7999. Via.
See also: trench digging problem.
Lusine - Two Dots
The original music Video… who had thought that an animated geometry lesson would make a great music video?
Reblogged from MEMEs that make me who I am
Circle geometry by justinandleah on Flickr.
Mascheroni construction of a unit square. More info and accompanying song here.
triskaidecagon by rikb000 on Flickr.
“A pretty good approximate geometric construction of the triskaidecagon, or 13 pointed star. Constructing the triskaidecagon exactly is impossible using the traditional rules of compass and straightedge construction, but this construction is close - it has a cumulative relative error of .7%, or 2.51 degrees. As far as I’m aware, I’ve invented this. Or, as Plato would have it, I’m the first one to remember it. I wouldn’t actually be surprised to find out that someone else has used this construction, because it’s very simple - but then again, there probably aren’t many people who go around trying to figure this kind of thing out. I’m also sure there are more precise constructions since one can do this with arbitrary precision, but they’re probably more complex.
First, draw a circle centered at A. Then construct the square BCDE inside the circle. Bisect the segment AF at G. The bisection will mark point H on the circle. Construct a circle centered at H with radius HG. This circle will encompass 5 points of the triskaidecagon. Construct a circle with center at J and radius JH, then draw line AK by connecting the points where circles H and J intersect. HL and JL are sides of the triskaidecagon. You can construct the remaining sides by stepping this radius around the circle. If you want to distribute the error more effectively than just stepping around the circle 13 times, you can use the point where an extension of HG crosses the circle and the point where the vertical diameter of the circle crosses the circumference as reference points to step from.
The angle HAL is 27.885567º, the angle subtended by the side of a perfect triskaidecagon is 27.692308.”
TSP art is a type of line art based on the Traveling Salesman Problem. An image is first discretized into black points on a white background. The points are then treated as “cities” in the TSP problem. An approximate solution to the TSP problem is calculated and drawn. The result is striking approximation to the original image. Remarkably, the path never crosses itself. Read more here.
(1/2)
Next »
About
Recreational mathematician and aspiring teacher. Grew up a math nerd and consider the subject a major part of my identity. Fascinated by just about everything. Here's hoping this blog will open me up to some more creative outlets. That might be good for me at this juncture in my life :)
