Tuesday, January 5th, 2010
How to Determine Dedekind Cuts
Description
A detailed tutorial on how to determine Dedekind cuts. Step by step tutorial including several examples of Dedekind cuts for reference.
Overview
A Dedekind cut is a partition of rational numbers into two non-empty sets A and B, such that all elements of A are less than elements of B, and A has no greatest element. The cut itself is a gap that is located between A and B, which is normally found by creating a new, irrational number, and setting it in the gap. What irrational number you use depends on what numbers you have partitioned into the two sets. It is like the number line of advanced algebra, that has both rational and irrational numbers on it instead of just integers. The Dedekind cut was named after Richard Dedekind.
Tags: algebra, between, cut, Dedekind, elements, empty, gap, greater, integer, irrational, less, line, non, non-empty, numbers, partition, rational, Richard, sets, than
Posted in Algebra | No Comments »
Tuesday, November 17th, 2009
Overview of Half-Circles
Description
A detailed tutorial on equations of a half-circle. Step by step tutorial including several examples and an explanation of half-circles for reference.
Overview
A half-circle is truely half of a circle. If you take a circle and cut it in half, you will get a half circle. Because of this, the equations of the half-circle are very similar to the equations of a full circle – simply divide the equation by two. The only ones that you cannot find that way are the radius, diameter, and circumference. The radius and diameter do not change on a half-circle. There is no circumference on the half-circle, but if you need the circumference for another formula you can use the circumference of the whole circle of that half-circle.
Tags: area, basic, circle, circumference, coordinates, cut, diameter, divide, equation, Geometry, half, half-circle, pi, radius, shape, split, two, whole
Posted in Geometry | No Comments »
