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The ABC’s of Math

The Oxford Concise Dictionary of Mathematics, edited by Christopher Clapham and James Nicholson, covers both pure and applied mathematics and statistics and includes linear algebra, optimization, nonlinear equations, and differential equations.  With over 3,000 authoritative entries it is a one-stop math resource.  Since I usually don’t deal with math I thought it would be fun to excerpt some entries.  Below are some samples from the “A”, “B”, “C”, “Q”, “R”, and “S” sections.  Enjoy!

Achilles paradox: The paradox which arises from considering how overtaking takes place.  Achilles gives a tortoise a head start in a race.  To overtake, he must reach the tortoise’s initial position, then where the tortoise had moved to, and so on *ad infinitum.  The conclusion that he cannot overtake because he has to cover an infinite sum of well-defined non-zero distances is false, hence the paradox.

Break-even point: The point at which revenue begins to exceed cost.  If one graph is drawn to show total revenue plotted against the number of items made and sold and another graph is drawn with the same axes to show total costs, the two graphs normal intersect at the break-even point.  To the left of the break-even point, costs exceed revenue and the company runs at a loss while, to the right, revenue exceeds costs and the company runs at a profit.

Cuboctahedron: One of the *Archimedean solids, with 6 square faces and 8 triangular faces.  It can be formed by cutting off the corners of a cube to obtain a polyhedron whose vertices lie at the midpoints of the edges of the original cube.  It can also be formed by cutting off the corners of an *octahedron to obtain a polyhedron whose vertices lie at the midpoints of the edges of the original octahedron.

QED: Abbreviation for quod erat demonstrandum.  Latin for ‘which was to be proved’.  Often written at the end of a proof.

Radius (radii): A radius of a circle is a line segment joining the centre of the circle to a point on the circle.  All such line segments have the same length, and this length is also called the radius of the circle.  The term also applies in both senses to a sphere.

Subtraction: The mathematical operation which is the inverse operation to *addition which calculates the difference between to numbers or quantities.  So 7-2=5, and (3x+5y)-(x+2y)=2x+3y.

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