Sum/product of consecutive numbers and other math shortcuts

If you have studied some of the old SAT questions at some point you may have gone through questions like –

4 consecutive numbers sum to 166. What is the product of the numbers? or…

3 consecutive even numbers sum to X. What is their product?

The way the tutors and the online tutorials show seems to always be to algebraically solve this – for example 4 consecutive numbers would solve x+x+1+x+2+x+3 = 166, collect terms and solve…

However there is another way that works for this and works for other similar problems.

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PyImageSearch Review

If you have been doing OpenCV or Python machine learning, you have most likely come across PyImageSearch. If you come across a sale for this service I would recommend trying it out if you are learning some machine learning. This past week they have run a free promo 7 day trial, which gave me an opportunity to browse these.

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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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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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