Shape Operator

A famous problem in approximation theory is to approximate the function \left|x\right| as accurately as possible on the interval -1 \le x \le 1, measured by maximum absolute error, using either polynomials or rational functions of fixed degree.

The geometric series, S_{n}(x) = \sum_{k=0}^{n} x^k, satisfies a linear recurrence S_{n+1}(x) = x \, S_n(x) + 1 with constant (in n) coefficients.

Newton’s iteration for computing the reciprocal of a, y_{n+1} = y_n(2-ay_n), can be derived by applying Newton’s method to the function f(y)=1/y-a.

For some reason, a six year old study claiming that dogs align with Earth’s magnetic field when they poop in “calm magnetic field conditions” is making the rounds online again.

In several recent posts, I have been exploring a way of doing trigonometry using vectors and their various products while de-emphasizing angle measures and trigonometric functions.

In previous posts, I have shown how to visualize both the dot product and the wedge product of two vectors as parallelogram areas.

A visual way of expressing that three vectors, a, b, and c, form a triangle is and an algebraic way is a + b + c = 0 In a previous post, I showed how to generate the law of cosines from this vector equation—solve for c and square both sides—and that this…

I recently posted a geometry puzzle about an autonomous lawn mower steered by a rope and a peg.

One of the joys of being an engineer at Desmos is that my collaborators occasionally bring me math problems that they need to solve to make something that they’re building work right.

I have a confession to make: I have always found symbolic algebra more intuitive than geometric pictures.