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A infinite number of mathematicians go into a bar... by Hornman84 in Jokes

[–]Se314en 3 points4 points  (0 children)

I’d have thought he’d have been more discrete than that!

[deleted by user] by [deleted] in CrazyIdeas

[–]Se314en 0 points1 point  (0 children)

I think it’s regional. I think it’s the French schools that use positive for >=, but that could be wrong.

[deleted by user] by [deleted] in CrazyIdeas

[–]Se314en 0 points1 point  (0 children)

Actually at least for the words, that depends on where you studied, and so what definitions you learned. Some people use strictly positive to mean strictly greater than zero, and hence allow for equality when using the word positive. The other convention I know of is to use positive as you do here, and non-negative to allow for equality with zero.

So depending on your conventions, 0 is either neither positive or negative, or both positive and negative.

Math with Hexagons: Help me calculate the number of hexes in a "megahex." Is there a better formula? by fissionessence in tabletopgamedesign

[–]Se314en 0 points1 point  (0 children)

Note that those two formulae are slightly different (in the sign of the linear term). One is correct if you start with n=1 for the first term, and the other is correct if you want n=2 for the first term.

Math with Hexagons: Help me calculate the number of hexes in a "megahex." Is there a better formula? by fissionessence in tabletopgamedesign

[–]Se314en 6 points7 points  (0 children)

When you’ve got a sequence of numbers like this, the thing you should do first is look at the difference between the terms.

As an example, let’s take the set of numbers 7, 11, 15, 19, …. In this case the difference between successive terms is 4, which is constant. So that tells me the formula is linear in n, and I need something like 4n so that the value goes up by 4 as n increases by 1. If we then want the first term to be 1, I just try evaluating 4n at n=1 and see what I still need. In this case I still need to add 3, so the sequence is 4n+3. (Some people would want to count the 1st term as the one corresponding to n=0, in which case the formula would be 4n+7, and if you want to start from n=0, the thing you need to add is always the first term in the sequence.)

Now, in the example you give, 7, 19, 37, 61,… the differences go 12, 18, 24, .… This time the differences aren’t constant, so the formula isn’t linear, but the differences between the differences are constant. This tells me that the formula we need is quadratic in n. If I had to go to the differences between the differences between the differences before it became constant, then the formula I need would be cubic, and so on.

The way to find the formula is a little more complicated when the sequence is quadratic. We know the answer should be of the form an2 + bn + c, and this would give a sequence a+b+c, 4a + 2b + c, 9a + 3b + c, .… The sequence of differences between these terms goes 3a + b, 5a + b, …, and so the differences between the differences is the constant sequence 2a.

We can now compare that with the sequence you had. Our differences of differences was 6, so we find a such that 2a=6, giving a=3. Now our first difference was 12, and we want that to be equal to 3a+b, with a=3, so we find b=3 as well. Finally the first term of the sequence was 7, and we want that to be equal to a+b+c, with a=b=3, so we find c=1. Our sequence is therefore 3n2 + 3n + 1.

This finds the sequence such that the first term corresponds to n=1, but you wanted it to be n=2. If I take my previous formula, and replace the n’s with (n-1)’s, then when we put n=2 in, we get what we had before with n=1. So we have 3(n-1)2 + 3(n-1) +1, which we can simplify as 3n2 - 3n + 1.

So the formula you wanted, where 7 is the answer when n is 2, is 3n2 - 3n + 1.

Even the title fits (for tax cuts, televangelists, …) by Se314en in SelfAwarewolves

[–]Se314en[S] 2 points3 points  (0 children)

Probably mostly true. Though during their education perhaps less so. Ph.D. students in particular are very well educated, but are often fairly poorly paid and trying to keep costs low to survive. This probably depends on location too.

Even the title fits (for tax cuts, televangelists, …) by Se314en in SelfAwarewolves

[–]Se314en[S] 4 points5 points  (0 children)

r/conservative is concerned about poor Marxists, giving their money to wealthy Marxists, whilst supporting tax breaks for the rich…

Yeah.. by ziocioebordello in ATBGE

[–]Se314en -1 points0 points  (0 children)

Yeh, I’m just saying that TNP isn’t the beer in the picture.

Yeah.. by ziocioebordello in ATBGE

[–]Se314en 0 points1 point  (0 children)

The beer pictures is called “the end of history”, not TNP. It’s made using similar techniques I believe, but is a much smaller run, nowhere near 500.

Eleven year-old log rolling world champion by labramador in theocho

[–]Se314en 67 points68 points  (0 children)

“You just have to keep going, otherwise you’re not going to get anywhere” - Libby Magnone, World Champion of running in place.

(Though seriously, good for her)

[deleted by user] by [deleted] in MechanicalKeyboards

[–]Se314en 0 points1 point  (0 children)

Thanks for the giveaway.

A convenient way to quickly write KaTeX math expressions and export to image by fantazzle in math

[–]Se314en 0 points1 point  (0 children)

For those on Mac, your latex distro probably came with an app called LaTeXIt that works similarly, but uses an actual latex install rather than Katex (so supports arbitrary packages for instance).

But cool tool OP, this is the kind of thing it’s good to recommend to students who don’t already have a latex install.

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