Category Archives: mathematica

Rigid bodies, formulation and examples

My friend Rhett Allain gave me a good challenge recently with this tweet: I had been working on a problem that he posted about regarding a bead sliding freely on a hoop that is spinning about an axis in its … Continue reading

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What’s my 30 mile cycle limit?

UPDATED WITH 4th APPROXIMATION! Last weekend I went hammock camping by towing all my gear behind my bike. I loved it and now I’m interested in finding other adventures that won’t tax me too much. I really think that, for … Continue reading

Posted in fun, math, mathematica, technology | 6 Comments

Brachistochrone for rolling things

The Brachistochrone curve is the shape of a wire for beads to slide down (friction free) to get from point A to point B the fastest. Note that since I used the word “down” there I’m implying this happens in … Continue reading

Posted in math, mathematica, physics, teaching | 2 Comments

Catenary with Lagrange Multipliers

The catenary is the shape of a hanging chain supported at both ends in a constant gravitational field (ie normal life). Recently Rhett Allain has been doing some great work using both python and analytical results to show how you … Continue reading

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Fast Quantum Tunneling Method

This post describes a way to calculate tunneling probabilities for one dimensional quantum barriers. This method is easy to code up, and is very fast. Consider the following barrier. If your energy is less than 3 eV, you’ll just reflect … Continue reading

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One die to rule them all

For a number of years I’ve been working on finding ways to turn what looks like an unfair die to a fair one (see these posts). Recently I’ve made a lot of progress. This post shows how I’ve turned a … Continue reading

Posted in fun, mathematica, physics, research | 4 Comments

Doppler Drum Corps

One of my favorite oral exam questions to give students in introductory physics classes is to ask them whether marching bands should worry about tuning because of the Doppler Effect (lots of details below but the short version: if there’s … Continue reading

Posted in fun, general physics, mathematica, parenting, physics | 6 Comments

Stable, asymmetric dice

A while ago I set about trying to find asymmetric dice that might be fair. I’ve put a lot more work into it, but mostly because there’s been a lot of frustrating interesting tangents. Here’s the main thrust of the … Continue reading

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Fair Asymmetric Dice, getting there

Ever since my son and I worked on whether different types of 20-sided dice were fair I’ve been thinking about whether there might be some oddly shaped dice that could still be fair.  I’ve watched these three numberphile videos and I’ve looked … Continue reading

Posted in fun, mathematica, physics | 7 Comments

Mass changing orbits

A few weeks ago my good friend John Burk posted some intriguing questions about what happens to planetary orbits as the sun loses mass (all that heat has to come from somewhere!). I’ve been thinking about it ever since and … Continue reading

Posted in general physics, mathematica, physics | 2 Comments