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There are many unsolved problems in mathematics. Some prominent outstanding unsolved problems (as well as some which are not necessarily so well known) include 1. The Goldbach conjecture . 2. The Riemann hypothesis .
Incircle of a Triangle Geometry construction using a compass and straightedge As can be seen in Incenter of a Triangle , the three angle bisectors of any triangle always pass through its incenter.
If an enormously heavy object has to be moved from one spot to another, it may not be practical to move it on wheels. Instead the object is placed on a flat platform that in turn rests on cylindrical rollers (Figure 1) . As the platform is pushed forward, the rollers left behind are picked up and put down in front. An object moved this way over a flat horizontal surface does not bob up and down as it rolls along. The reason is that cylindrical rollers have a circular cross section, and a circle is closed curve "with constant width."
Clever student: I know! Now we just plug in x=0, and we see that zero to the zero is one! Cleverer student: No, you’re wrong! You’re not allowed to divide by zero, which you did in the last step.
Weierstrass functions are famous for being continuous everywhere, but differentiable "nowhere". Here is an example of one: It is not hard to show that this series converges for all x . In fact, it is absolutely convergent . It is also an example of a fourier series , a very important and fun type of series.
This is a series of videos about doodling in math class. Hopefully more info about the mathematics soon. For other videos, see this page . To download a video, right click and select "save link as" (or something like that, depending on your browser).