## Mathematicians submit proof of Erdős Coloring Conjecture

Fifty years ago, several mathematicians at a dinner party were discussing graphs (points and lines, not chart graphs), and the generalization if you make the edges connecting a point (vertex) with another, able to connect multiple points. While working out the minimal number of colors in general, they found it to be an interesting problem, to test out and prove the next day… Well, that solution, to Erdős, Faber, and Lovász’ problem was delayed for years and years!

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## Happy Pi day 2021!

Happy Pi day! Hope you are enjoying making pie (within your household/pod) and learning some new math stuff today! Matt Parker has an interesting video up on an attempting to calculate pi from a diameter of one-molecule thick droplet spreading on water:

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## Injecting commands and debugging a running Python program, with Project Euler example

How often has it happened to you… you build a simple script to calculate something, run some bulk process, and coming back after an hour or so it just hangs with no output. Is it doing something or stuck? You could debug it, using WinPdb or Visual Studio Code debugger or GDB to run it step by step, but that would lose the time that it has been processing. Instead, you can use Pyrasite, a program for looking in to a running Python script!

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## Machine learning SVM – the usefulness of kernels

If you’ve read through how Support Vector Machines work, you probably know the linear simple SVM might not work in all cases… but how does it fail? Let’s take a look at an example I tried like to my simple example… but change it to be a larger space than just 4, and separated with a region in the middle, and the region around it (positive, negative labelled areas to learn):

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## Human pose estimation with Python and Gluoncv

Human pose estimation is something useful for robotics/programming as you can see what position a person is in a picture. For last weekend’s Hackrithmitic I did an experiment for fun using computer vision pose estimation. To start with I found several possibilities with available libraries:

• Tensorflow js has been used to say, don’t touch your face, but it takes a massive amount of cpu.
• Openpose is a popular one, only licensed for noncommercial research use, and there is a Opencv example for it that doesn’t quite show how to use it.
• AlphaPose is supposedly faster and has a more clear license and possibility for commercial use – if you want that as a possibility. I checked out the install instructions and worked but for “python3” instead of “python”. It also misses obvious step of installing cuda for your Nvidia system before running.
• GluonCV is another, which seems more user friendly. This one I was able to get running in a few minutes with their example:
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## Slide rule enters the 21st century

Some time ago I came across this online tool in a newsletter article – this is a very cool slide-rule-emulator that will not just let you move two slides, but actually slide it for you as you run an equivalent digital calculator calculation to the right!

If you haven’t ever used a slide rule before, it works on properties of logarithms, and the principle that log(a)+log(b) = log(a*b). Now it wouldn’t be very interesting to just have two normal rulers together, as sliding and adding would just let you do problems like 5+5 = 10 or 50+50 = 100 if you scale the numbers. With logarithmic scale, the spacings are off and it allows you to do multiplication in adding the numbers.

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## Microsoft Math Solver review

Years ago if you wanted a program to explain steps in mathematics, algebra or other complex math as a tutor would, you would have to buy a specialized software package built for some specific operating system (I forget the name… it may still be around?) Of course there was always open source software like Maxima to do powerful symbolic (or numeric, or graphing) math, but to know what to do one almost needs a manual, and while extremely powerful it was not helpful for beginners. I recently found a similarly useful free math solver on Microsoft’s site, https://mathsolver.microsoft.com:

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## Possible ABC Proof Conjecture brings Primes into Prime time news again!

Recently a possible proof of the ABC Conjecture has been in the news. Although the proof of this is hundreds of pages long and not really a fun read for most people, this reminded me of the prime spiral, “Ulam spiral” which we explored years ago at a meetup.

The interesting thing about ABC Conjecture is that no matter what examples or counterexamples you find to the inequality, it does not prove or disprove the theory as to where there are only finitely many specific triples to solve the inequality.

Ulam’s spiral is also a look into prime numbers, but from a visual perspective. Nothing to “prove” here but to see an interesting pattern within numbers. It was supposedly thought of by Stanislaw Ulam during a meeting, doodling numbers, and it was later popularized by Martin Gardner’s writings. It is a great way to have some fun learning how to use Matplotlib to draw up some interesting charts, too:

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## Mathematics with Pi – and earth measurement with network requests

In Ian Stewart’s book, Professor Stewart’s Casbook of Mathematical Mysteries, he writes about an easy way one might prove that the earth is not flat. His “easy” proof can be done by booking some flights and timing them… or, simply looking up actual flights from certain cities to other cities. If it is much much shorter for a certain flight from A to D while A to B to C to D in a nearly straight line is much longer, it’s effectively a proof you can go around the world without falling off…

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