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nsato7.bsky.social @nsato7.bsky.social · 27/09/2026

Rhombic Tiling of a Regular Polygon www.desmos.com/calculator/y... #iTeachMath @desmos.com

nsato7.bsky.social @nsato7.bsky.social · 17/09/2026

Suppose you take k points in the interval [0,2π] (spaced apart by 2π/k) and map them to the rose curve r = cos nθ. Then you can get interesting looking graphs - and sometimes, a regular polygon. (Thanks to @helsig.bsky.social for the idea.) www.desmos.com/calculator/g... #iTeachMath @desmos.com

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nsato7.bsky.social @nsato7.bsky.social · 29/08/2026

You can test whether a number n is divisible by 7 using the attached graph. Start at the bottom node. For each digit d in n (starting with the left digit), move along the black arrows d times. Each time you go to the next digit, move along a white arrow. #iTeachMath

Graph with 7 nodes, and black and white arrows.

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nsato7.bsky.social @nsato7.bsky.social · 03/07/2026

I proved a theorem about a quadrilateral which turned out to be obvious. You could say it was a 4-gon conclusion. #iTeachMath

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nsato7.bsky.social @nsato7.bsky.social · 29/06/2026

I have been thinking about Mobius transformations, and how to visualize them. Using Desmos Notebook, I can connect their 2D and 3D representations. www.desmos.com/notebook/ssd... @desmos.com #iTeachMath

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nsato7.bsky.social @nsato7.bsky.social · 23/05/2026

From www.boredpanda.com/funny-textbo...: The Patrick Star graph! #iTeachMath

Graph of z = x^4 + y^4 - 4xy + 1 extended to Patrick Star.

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nsato7.bsky.social @nsato7.bsky.social · 15/05/2026

Interference Pattern www.desmos.com/calculator/g... @desmos.com #iTeachMath

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nsato7.bsky.social @nsato7.bsky.social · 12/05/2026

For an ellipse, it's clear which part is the "inside" and which part is the "outside". For a hyperbola, which part is the "inside"? Which part is the "outside"? #iTeachMath

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nsato7.bsky.social @nsato7.bsky.social · 25/03/2026

Take a number where the digits are increasing from left to right, and digits can repeat, like 134446689. If we multiply it by 9, then we get 1210020201. The sum of the digits of the new number is 1 + 2 + 1 + 0 + 0 + 2 + 0 + 2 + 0 + 1 = 9. Does this always happen? #iTeachMath

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nsato7.bsky.social @nsato7.bsky.social · 20/02/2026

For a positive integer n, let f(n) = sin(1) + sin(2) + ... + sin(n), where sin is measured in radians. Plotting the values of f gives us a graph with some interesting structure. www.desmos.com/calculator/l... As a challenge, try to find the best bounds on f. @desmos.com #iTeachMath

Plot of the function f(n) = sin(1) + sin(2) + ... + sin(n)

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nsato7.bsky.social @nsato7.bsky.social · 16/02/2026

I was gifted a gorgeous origami sculpture of five intersecting tetrahedra. This inspired me to recreate it using Desmos. www.desmos.com/3d/m7hqyu2gpr en.wikipedia.org/wiki/Compoun... @desmos.com #iTeachMath

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nsato7.bsky.social @nsato7.bsky.social · 26/01/2026

An ellipse rotates so that it stays in contact with the coordinate axes. What curve does the center of the ellipse trace? (If you are feeling ambitious, you can try finding the curve the foci trace, and its area.) www.desmos.com/calculator/v... #iTeachMath @desmos.com

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nsato7.bsky.social @nsato7.bsky.social · 25/10/2025

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

Triangle ABC with squares AB B1 B2 and AC C1 C2 on sides AB and AC. M is the midpoint of B1 and C1.

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nsato7.bsky.social @nsato7.bsky.social · 13/10/2025

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

Diagram of tetrahedron, octahedron, and cube in spheres.

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nsato7.bsky.social @nsato7.bsky.social · 19/05/2025

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

Photo of tire hubcaps with different kinds of symmetry.

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nsato7.bsky.social @nsato7.bsky.social · 09/03/2025

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

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Reposted by @nsato7.bsky.social

Karen Campe @karencampe.bsky.social · 08/03/2025

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

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nsato7.bsky.social @nsato7.bsky.social · 05/03/2025

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

In the coordinate plane, A = (a,0), B = (0,b), and C = (p,q).

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nsato7.bsky.social @nsato7.bsky.social · 22/02/2025

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

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nsato7.bsky.social @nsato7.bsky.social · 01/01/2025

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

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nsato7.bsky.social @nsato7.bsky.social · 31/12/2024

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

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nsato7.bsky.social @nsato7.bsky.social · 26/12/2024

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

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nsato7.bsky.social @nsato7.bsky.social · 19/12/2024

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

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nsato7.bsky.social @nsato7.bsky.social · 16/12/2024

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

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nsato7.bsky.social @nsato7.bsky.social · 13/12/2024

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

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