Some people need more help than others. #iTeachMath

Given triangle ABC, we construct squares AB B1 B2 and AC C1 C2 on the sides. Let M be the midpoint of B1 and C1. As point A varies, what do you notice about the position of point M?

www.desmos.com/calculator/3...

@desmos.com #iTeachMath

Suppose we want to arrange N points on a sphere, so that the smallest distance between any two points is maximized. For N = 4, 6, 8, we can take a regular tetrahedron, regular octahedron, and cube, respectively.

One of these is not the optimal solution. Which one?

#iTeachMath

While out on a walk, I noticed that the hubcaps on tires have very different kinds of symmetry. What kind of symmetry does your car have? What about the cars around you? #iTeachMath

Table of Lissajous Curves www.desmos.com/calculator/z...

I've seen this animation online, so I thought I'd try building it myself.

@desmos.com #iTeachMath

Trig is like an acquaintance who introduces themselves as being about triangles.
When you really get to know them, their real identity is uncovered: they are about circles (more specifically about triangles inside circles w/base a radius from center edge)
#iTeachMath

In the diagram below, triangle ABC is equilateral.

Given a and b, can you find p and q?

Given p and q, can you find a and b?

#iTeachMath

Three congruent circles are inscribed in a triangle, as shown below. Can you compute the common radius? www.desmos.com/calculator/p... @desmos.com #iTeachMath

What is the sum of all the numbers in the 9 times 9 table below? #iTeachMath

I have been thinking about how Desmos can show multiple representations on the same graph.

For example, suppose we cut a sector out of a circle with radius 1. We then roll the sector into a cone. What is the maximum volume of the cone?

teacher.desmos.com/activitybuil...

@desmos.com #iTeachMath

Apollonian Gasket www.desmos.com/calculator/e... @desmos.com

The Simson Line www.desmos.com/calculator/x... @desmos.com

Nested Hypocycloids www.desmos.com/calculator/l... @desmos.com

Poncelet's Theorem www.desmos.com/calculator/g... @desmos.com