Tag: mathematics

I learned about cycling-related Eddington numbers recently.

They are the largest integer n such that you have ridden at least n kilometers on at least n days (not necessarily consecutively).

I wrote some code to find mine.

With data from 2001 to 2024, my Eddington number is 102.

So, I rode at least 102 kilometers on at least 102 days, and have not ridden at least 103 kilometers on at least 103 days. Apparently, I've ridden at least 103 kilometers on 101 days, so I'll need to do that twice more to get my Eddington number up to 103. Sounds like a nice goal for 2025.

One can also use miles. An amusing thing to note is that you cannot simply convert the Eddington number in kilometers to the Eddington number in miles, since we're counting days.

My Eddington number in miles is 68. 68 miles is about 109 kilometers, so my Eddington number in miles is both larger and smaller than my Eddington number in kilometers.

One can, of course, apply this to running, walking, swimming, or really any other quantifiable activity.

Let me know if you'd like the (simple) code I wrote to calculate these.

My latest chapbook/zine: Complete Incomplete Cubes (after Sol Lewitt) contains all 4096 incomplete (plus "blank" and complete) cubes on 16 pages. Let me know if you'd like one and I'll mail a copy to you!

Updated my dice problem collection. The new problem is problem 40: A die is rolled and summed repeatedly until the sum is 100 or more. What is the most likely last roll? What if we roll two dice at time? Three, etc.?

If one die is rolled, then 6 is the most likely last roll, while 7 is the most likely last roll when two dice are rolled. With three dice, the most likely last roll is 12, but for more dice, a very clear pattern emerges: if the number of dice rolled is odd, then the most likely last roll is the most likely roll (greater than the median), while for an even number of dice, it is one more than the most likely roll. (Here we assume a sufficiently large value for "100": for large numbers of dice, we want to extend the threshold so the analysis is smoother.)

Just updated my Collection of Dice problems with a problem suggested by a reader (it's #27 of the now 78 problems).

Collection of Dice Problems

Giant image showing 63 different flavors of truchet tilings: all non-empty possibilities with 6 base tiles. Random flood filling added for color. Click to enlarge.

A new video, again using particles and circles. Made with Csound and processing.org.

Made some animations to demonstrate some theorems about octagons. I think they look pretty nice.

I was wanting to pack superellipses tightly, so I worked out how to get two of them to be tangent to each other, and this allows me to create superellipses that are as large as possible and so fill space well. For this image, I turned off the requirement that the superellipses not be inside one another, and I think it has a nice look to it.

These are all 4-exponent superellipses (i.e., their shapes are the same as that of x⁴+y⁴=1).