## Dancing and Mathematics? Really?

Sometimes, mathematics appears in places that we sometimes least expect it to be — like in dancing.

Although the figure above is bit of a stretch, Erik Stern (educator, choreographer) and Karl Shaffer (choreographer and mathematician) from     John F. Kennedy Center for the Performing Arts in Washington literally integrated mathematics and dancing in what they called Math Dance. In Math Dance, a class looks like a dance lesson, but it is also a new way  of teaching mathematics.  Math Dance involves translating patterns into choreography and translating patterns to mathematics.  Some of the mathematics learned in math dance are polyhedral geometry, symmetry, the mathematics of rhythm, and variations on dissection puzzles such as tangrams.

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Image Source: Unknown (please inform me about its origin if you know).

## 11 Proven Proof Techniques Non-Math Majors Should Know

Proofs is the heart of mathematics.  It is what differentiates mathematics from other sciences.  In mathematical proofs, we can show that a statement is true for all possible cases without showing all the cases. We can be certain that the sum of two even numbers is  even without adding all the possible pairs.

For those who are “non-math people,” the proof techniques below will help you, but the “math people” are probably those who are going to enjoy them more.  » Read more

## The 0.0001 Time Rate Approach, an Extended Application

In the previous post, I introduced to you the 0.0001 Time Rate approach This post is an extended application of the said technique on curvatures and radius of curvatures.

Curvature is defined (by The Facts on File Dictionary of Mathematics) as the rate of change of the slope of the tangent to a curve. For each point on a smooth curve there is a circle that has the same tangent and the same curvature at that point. The radius of this circle called the “radius of curvature”, is the reciprocal of the curvature, and its center is known as the center of curvature. If the graph of a function y=f(x) is a continuous curve, the slope of the tangent at any point is given by the derivative dy/dx and the curvature is given by

$C = \displaystyle\frac{\displaystyle\frac{d^2y}{dx^2}}{(1+(\displaystyle\frac{dy}{dx})^2)^{3/2}}$

and the radius of curvature is given by

$RC = \frac{1}{C} = \displaystyle \frac{(1+(\displaystyle \frac{dy}{dx})^2)^{3/2}}{\displaystyle \frac{d^2y}{dx^2}}$

where: $\frac{dy}{dx}$ is the derivative of $y$ with respect to $x$ and $\frac{d^2x}{dx^2}$  is the second derivative of y with respect to x or in simpler terms, it is the derivative of $\frac{dy}{dx}$. » Read more

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