Manifold of points: * see Endnote 47

a topological space that locally resembles Euclidean space near each point.  Topological space is a set of points, along with a set of neighbourhoods for each point, satisfying a set of axioms (a statement taken to be true or a premise; in Euclidean geometry there are 5 premises) relating points and neighbourhoods.  A point is a unique location in Euclidean space.  A neighbourhood of a point is a set of points containing that point where one can move some amount away from that point without leaving the set.

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angular functions: *  see Endnote 48

(aka trigonometric functions) relate the angles of a triangle to the lengths of its sides; important in the study of triangles and modelling periodic phenomena, and has many other applications.  The most familiar trigonometric functions are the sine, cosine, and tangent.

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periodic functions:

one that that repeats its values in regular intervals or periods; most important examples are the trigonometric functions, which repeat over intervals of 2π radians; are used throughout science to describe oscillations, waves, and other phenomena that exhibit periodicity.

 

Napierian base e:

(aka e) mathematical constant (approximately 2.71828), irrational number (not a ratio of integers), appearing in many different mathematical studies; discovered in 1683 by the Swiss mathematician Jacob Bernoulli while studying compound interest;  where e arises as the limit of (1 + 1/n)^n as n approaches infinity. The number e can also be calculated as the sum of the infinite series; important in mathematics, alongside 0, 1, π and i, which all play important & recurring roles.