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A Zometool Thanksgiving

While cleaning up after a successful group build, a colleague and some students had fun making a little Thanksgiving tribute in Zometool.

Zome Turkey

 

Derivatives of Vector Functions

Desmos -- Derivatives of Vector Valued FunctionsOne way to think of a curve in the plane (or in space) is as a collection of terminal points of vectors whose initial points are all at the origin.  The vectors are given by a vector-valued function.

For example, the parabola shown at right can be thought of as the graph of the vector-valued function

r(t) = < t , (t-1)^{2}+1>

I’ve created a Desmos demonstration that shows how graphs of vector-valued functions are related to their vectors (shown in blue), and how the derivative of a vector-valued function is related to both difference vectors and tangent vectors.  You can access the demonstration here.

You can find more of my Desmos demonstrations here.

Math Photo: Undersea Rose Curve

Undersea Rose Curve

I can’t look at this lovely jellyfish without seeing a four-petal rose curve in the polar plane.

four-petal rose curve

Exponentials and Ebola

My latest piece for the New York Times Learning Network is a lesson on the underlying mathematics of the spread of contagious diseases, like Ebola.ebola map

In this lesson, students use a basic exponential model to explore the fundamental mathematical ideas of transmission and replication.

Mathematically, the spread of disease can be modeled in a manner similar to the spread of a rumor. Although a number of simplifying assumptions must be made, the simple exponential model captures the basic impact of transmission rates on the dispersion of a disease among a population. Students can explore the consequences of transmission rate using multiplication, algebra, graphing utilities and elementary statistics.

After exploring the essential behavior of various simple exponential models, students then compare real-world data to their theoretical models.  Those that are capable can perform regressions on the data to approximate actual transmission rates.  The students’ work and the real-world data establish a context for discussing the strengths and weaknesses of this simple model of disease transmission.

This lesson is part of a series of Ebloa lessons at the NYT Learning Network and is freely available here.

Math Art: Twilight on Mars

I was playing around in Scratch this weekend, experimenting with some numerical methods for approximating integrals, when this lovely image unexpectedly emerged.  I call it Twilight on Mars.

Integration Art

Twilight on Mars

Looks like I’ve got a new math and art project for students, and me, to explore!