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The Jacobsthal numbers are the numbers obtained by the U_ns in the Lucas sequence with P=1 and Q=-2, corresponding to a=2 and b=-1. They and the Jacobsthal-Lucas numbers (the ...

On the Clebsch diagonal cubic, all 27 of the complex lines present on a general smooth cubic surface are real. In addition, there are 10 points on the surface where three of ...

An algebraic variety over a field K that becomes isomorphic to a projective space.

The identity function id(x) is the function id(x)=x which assigns every real number x to the same real number x. It is identical to the identity map. The identity function is ...

The unique nonnegative square root of a nonnegative real number. For example, the principal square root of 9 is 3, although both -3 and 3 are square roots of 9. The concept ...

All lengths can be expressed as real numbers.

Consider the plane quartic curve X defined by x^3y+y^3z+z^3x=0, where homogeneous coordinates have been used here so that z can be considered a parameter (the plot above ...

The Ree group R(q) is the automorphism group of a S(2,q+1,q^3+1) Steiner system.

Let F be a finite field with q elements, and let F_s be a field containing F such that [F_s:F]=s. Let chi be a nontrivial multiplicative character of F and chi^'=chi ...

A real number that is b-normal for every base 2, 3, 4, ... is said to be absolutely normal. As proved by Borel (1922, p. 198), almost all real numbers in [0,1) are absolutely ...