Langley’s Adventitious Angles Langley’s Adventitious Angles Langley’s Adventitious Angles is a mathematical problem posed by Edward Mann Langley in "The Mathematical Gazette" in 1922. In its original form the problem was as follows: formula_1 is an isosceles triangle. A solution was developed by James Mercer in 1923. This solution involves drawing one additional line, and then making repeated use of the fact that the internal angles of a triangle add up to 180° to prove that several triangles drawn within the large triangle are all isosceles. Many other solutions are possible. Cut the Knot list twelve different solutions and several alternative problems with
Zero degrees of freedom Zero degrees of freedom In statistics, the non-central chi-squared distribution with zero degrees of freedom can be used in testing the null hypothesis that a sample is from a uniform distribution on the interval (0, 1). This distribution was introduced by Andrew F. Siegel in 1979. The chi-squared distribution with "n" degrees of freedom is the probability distribution of the sum where However, if and formula_4 are independent, then the sum of squares above has a non-central chi-squared distribution with "n" degrees of freedom and "noncentrality parameter" It is trivial that a "central" chi-square distribution with zero degrees of freedom