Fractions without Quotients: Arithmetic of Repeating Decimals

Article by Plagge, Richard

In collections: Notation and conventions, Unusual arithmetic, Easily explained

URL: https://www.maa.org/sites/default/files/pdf/upload_library/22/Polya/00494925.di020680.02p0417i.pdf

Entry: http://read.somethingorotherwhatever.com/entry/Plagge1978

I just noticed a fact that I hadn't seen before, which I'll illustrate with two examples:

\[ \begin{vmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{vmatrix} = 0 \]

\[ \begin{vmatrix} 0 & 1 & 2 \\ 3 & 6 & 9 \\ 12 & 16 & 20 \end{vmatrix} = 0 \]

What's the pattern?

I quite liked @ColinTheMathmo’s entry to #BigMathOff: a simple, initially counterintuitive result that becomes intuitively obvious after a quick think! I wonder how many totally different ways there are to prove it.

If you haven’t yet, go read about it and beautiful Penrose tilings: http://aperiodical.com/2018/07/the-big-internet-math-off-round-1-edmund-harriss-v-colin-wright/

"I like to add � and â€™ any time I submit online forms because I know that some developer is going to see it and wonder if they have a bug"

https://twitter.com/tenderlove/status/722565868719177729

A real sight to see is someone who has been told the UK uses the metric system their entire lives and then they get here and everything is in miles and feet and they start to realise the extent to which we are absolute lads

Match 2 of the #bigmathoff is finely balanced, 72 to 70 - your vote could make the difference :

http://aperiodical.com/2018/07/the-big-internet-math-off-round-1-samuel-hansen-v-paul-taylor/

@monorail

you may think you have defated me

you've broken every rule, crossed every line

but I have studied every single board

every permutation

every. possible. turn.

I WILL NOT BE DEFEATED

@monorail impressive, but while youre tackling this head-on, i was really playing in 𝐓𝐇𝐄 𝐓𝐇𝐈𝐑𝐃 𝐃𝐈𝐌𝐄𝐍𝐒𝐈𝐎𝐍

The graphs of cos(x) and tan(x) intersect at right angles - who knew ?!? More, have a look at the gradients - *very* interesting.

If someone with a disability or a chronic illness or a mental illness tells you something is too difficult for them to do, believe them. Maybe it's something they could do on another occasion. Maybe it's something you find, or even "everyone" finds, easy. Maybe it's something you found trivial to research or learn how to do. Believe them anyway. Maybe it's only three steps, maybe it's a piece of software, or a phone call. Believe them anyway.

Believe people when they tell you their experiences.

On Fibonacci Quaternions

Article by Serpil Halici

In this paper, we investigate the Fibonacci and Lucas quaternions. We give the generating functions and Binet formulas for these quaternions. Moreover, we derive some sums formulas for them.

URL: https://link.springer.com/article/10.1007/s00006-011-0317-1

Entry: http://read.somethingorotherwhatever.com/entry/OnFibonacciQuaternions

Thanks to UKClimbing.com I had a database of over 427k rock climbing routes to feed to a neural network. It did pretty well. http://aiweirdness.com/post/175339699997/blue-boulders-problem-1-more-rock-climbing-routes

Will augmented reality let me see the fractal, paper-thin region of space where an automatic faucet senses my hands?

This paper shows, among other things, that no hexagonal number is double another hexagonal number: https://arxiv.org/abs/1806.07981v1

New entry!

When are Multiples of Polygonal Numbers again Polygonal Numbers?

Article by Jasbir S. Chahal and Nathan Priddis

In collection: Easily explained

Euler showed that there are infinitely many triangular numbers that are three times another triangular number. In general, as we prove, it is an easy...

URL: http://arxiv.org/abs/1806.07981v1

PDF: http://arxiv.org/pdf/1806.07981v1

Entry: http://read.somethingorotherwhatever.com/entry/WhenareMultiplesofPolygonalNumbersagainPolygonalNumbers

I'm running a four-round instant knock-out tournament throughout the month of July to basically squeeze a load of fun maths out of my friends. Let's see if we can make it all come together! Voting starts on the 1st of July.

http://aperiodical.com/2018/06/announcing-the-big-internet-math-off/

Sometines I have a really hard time telling 0 and 1 apart.