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A point is a 0-dimensional mathematical object which can be specified in n-dimensional space using an n-tuple (x_1, x_2, ..., x_n) consisting of n coordinates. In dimensions ...
Limacon of Pascal
The dual of Brianchon's theorem (Casey 1888, p. 146), discovered by B. Pascal in 1640 when he was just 16 years old (Leibniz 1640; Wells 1986, p. 69). It states that, given a ...
Pascal's triangle is a number triangle with numbers arranged in staggered rows such that a_(nr)=(n!)/(r!(n-r)!)=(n; r), (1) where (n; r) is a binomial coefficient. The ...
The lines containing the three points of the intersection of the three pairs of opposite sides of a (not necessarily regular) hexagon. There are 6! (i.e., 6 factorial) ...
Each subsequent row of Pascal's triangle is obtained by adding the two entries diagonally above. This follows immediately from the binomial coefficient identity (n; r) = ...
Three types of n×n matrices can be obtained by writing Pascal's triangle as a lower triangular matrix and truncating appropriately: a symmetric matrix S_n with (S)_(ij)=(i+j; ...
A point which is a member of the set closure of a given set S and the set closure of its complement set. If A is a subset of R^n, then a point x in R^n is a boundary point of ...
"God is or He is not...Let us weigh the gain and the loss in choosing...'God is.' If you gain, you gain all, if you lose, you lose nothing. Wager, then, unhesitatingly, that ...
A point which lies on at least one ordinary line is called an ordinary point, or sometimes a regular point.
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