I've come up with an alternative for beziers that might be easier to ray-trace, perhaps even though a plain vertex shader. Though I'm missing a function there. I need to find the …

On Pages 1-3 of Cours 2 of Toën's Master Course on Stacks, he defines the notion of a Geometric context with a rather extensive list of axioms (they take up about two pages over an …

The most well known case of Routh's triangle theorem is: If the sides BC, CA,and AB are trisected at the points D, E, and F, respectively, then the area of the inside triangle for …

is a tent like shape a rectangular based prism or a triangular based prism. need answer before 17th of march 2010 (befor 16th for america)

If a four-legged, rectangular table is rickety, it can nearly always be stabilised just by turning it a little. This is very useful in everyday life! Of course it relies on the flo …

Because the theory of sheaves is a functorial theory, it has been adopted in algebraic geometry (both using the functor of points approach and the locally ringed space approach) as …

Suppose we have a surface S (although the question might make as much sense in higher dimensions) and a topological group G. The data of a flat vector bundle on S (up to isomorphis …

Let $K(r)$ be the piecewise function                        &nbs …

I am looking for an analogue for the following 2 dimensional fact: Given 3 angles $\alpha,\beta,\gamma\in (0;\pi)$ there is always a triangle with these prescribed angles. It is s …

Computing the volume of a sphere is straightforward 4/3*pi*R^3 As is the volume of a rectangular space length*width*height (e.g. 10*10*6) How might I go about determining how man …

Prove that if H is the union of a finite number of unit squares in the plane, then the ratio of the perimeter and the area of their union is at most four. Remarks. If the squares …

Suppose theta and d are given. How big can a set of d-dimensional vectors be such that no pair of them are at angle less than theta? I particularly want an upper bound; that is, …

Do any treatises on real analysis take the following as the basic completeness axiom for the reals? "Let $A$ and $B$ be set of real numbers such that (a) every real number is eith …

Let E be an ellipse centered at the origin on the x, y plane with major radius b and minor radius a. The length of the shortest line segment tangent to E that begins on the x-axis …

Is 'small enough' ellipse projected on a surface of a sphere convex? By ellipse I mean a set of points 'C' with a constant sum |AC| + |BC|, A and B are the centers. By 'small enoug …