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The only linear associative algebra in which the coordinates are real numbers and products vanish only if one factor is zero are the field of real numbers, the field of ...

The Pell-Lucas numbers are the V_ns in the Lucas sequence with P=2 and Q=-1, and correspond to the Pell-Lucas polynomial Q_n(1). The Pell-Lucas number Q_n is equal to ...

The Pell-Lucas polynomials Q(x) are the w-polynomials generated by the Lucas polynomial sequence using the generator p(x)=2x, q(x)=1. The first few are Q_1(x) = 2x (1) Q_2(x) ...

The Pell constant is the infinite product P = 1-product_(k=0)^(infty)(1-1/(2^(2k+1))) (1) = 1-(1/2;1/4)_infty (2) = 0.58057755820489... (3) (OEIS A141848), where (a,q)_infty ...

A special case of the quadratic Diophantine equation having the form x^2-Dy^2=1, (1) where D>0 is a nonsquare natural number (Dickson 2005). The equation x^2-Dy^2=+/-4 (2) ...

The Pell graph Pi_n is the graph defined as follows. Consider n-tuples of (0,1,2) such that maximal blocks of an odd number of 2's are forbidden. Take these as the vertices ...

The Pell numbers are the numbers obtained by the U_ns in the Lucas sequence with P=2 and Q=-1. They correspond to the Pell polynomial P_n(x) and Fibonacci polynomial F_n(x) ...

The Pell polynomials P(x) are the W-polynomials generated by the Lucas polynomial sequence using the generator p(x)=2x, q(x)=1. This gives recursive equations for P(x) from ...

The set of all lines through a point. The term was first used by Desargues (Cremona 1960, p. x). The six angles of any pencils of four rays O{ABCD} are connected by the ...

The lines of a pencil joining the points of a line segment range to another point.