Search Results for ""

As used in physics, the term "exact" generally refers to a solution that captures the entire physics and mathematics of a problem as opposed to one that is approximate, ...

In a given acute triangle DeltaABC, find the inscribed triangle whose perimeter is as small as possible. The answer is the orthic triangle of DeltaABC. The problem was ...

The discontinuous solution of the surface of revolution area minimization problem for surfaces connecting two circles. When the circles are sufficiently far apart, the usual ...

The branch of algebraic topology which deals with homotopy groups. Homotopy methods can be used to solve systems of polynomials by embedding the polynomials in a family of ...

Find the surface enclosing the maximum volume per unit surface area, I=V/S. The solution is a sphere, which has I_(sphere)=(4/3pir^3)/(4pir^2)=1/3r. The fact that a sphere ...

Given the "peaks" of three equilateral triangles placed on the sides of a triangle T, construct T. The problem was proposed by Lemoine (1868) and solved for the general case ...

A convex figure constructed by iteratively halving the base of an equilateral triangle and then sliding adjacent triangles so that they slightly overlap. Combining several ...

The problem of polygon intersection seeks to determine if two polygons intersect and, if so, possibly determine their intersection. For example, the intersection of the two ...

The solution u(x,y)=int_0^xdxiint_1^yR(xi,eta;x,y)f(xi,eta)deta, where R(x,y;xieta) is the Riemann function of the linear Goursat problem with characteristics phi=psi=0 ...

The function f(x,y)=(1-x)^2+100(y-x^2)^2 that is often used as a test problem for optimization algorithms (where a variation with 100 replaced by 105 is sometimes used; ...