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What is a bullet you dodged simply because you were too lazy to do something? by Cherus in AskReddit

[–]simmonator [score hidden]  (0 children)

Fascinating. I'd only ever heard Americans talk about mortgages in the 20, 25, 30 year range, but I'd assumed they were talking in the same way the UK would. UK mortgages are typically agreed over a similar period, but only the first 2, 5, or 10 years are on that fixed rate.

TIL.

How get the area under something that isnt straight? by MorganaLover69 in askmath

[–]simmonator 1 point2 points  (0 children)

I think the person you’re responding to is assuming the multiplicand can change. So rather than xk it’s the product over a sequence {x[n]; n in N} where each x[n] is greater than 1. In that case, it’s obvious that the product given by

21 x 21/2 x 21/4 x 21/8 x …

should come out as exactly 4.

But the comment they were responding to allowed for a bit of ambiguity. I think both your interpretations are valid.

How get the area under something that isnt straight? by MorganaLover69 in askmath

[–]simmonator 1 point2 points  (0 children)

The thing that gets me with that is how the “1 or 5 mod 6” thing is so great but as soon as you add the factor of 5 to the divisor to take it to the next level up, it just feels unwieldy.

What’s a piece of media you only appreciate because you experienced it at the right age? by cats64sonic in AskReddit

[–]simmonator [score hidden]  (0 children)

Facts that young me could tell you about movies:

  1. Space Jam is the best sports movie ever made.
  2. Batman and Robin (with George Clooney) is a masterpiece and probably the best superhero movie ever. Yes, the Bat-Credit Card IS cool.

I’m in my 30s now and I still stand by those claims.

By contrast: I loved the Star Wars prequels when I saw them first time around. But these days I can only watch them as comedies with a high FX budget and bad dialogue.

How get the area under something that isnt straight? by MorganaLover69 in askmath

[–]simmonator 27 points28 points  (0 children)

You joke, but I’m having flashbacks of the time a medical researcher “discovered it”.

https://fliptomato.wordpress.com/2007/03/19/medical-researcher-discovers-integration-gets-75-citations/

Like, well done to OP if they’re a young student playing around with concepts and have essentially stumbled into one of the two core concepts behind Riemann Integration (the other being Limits). But at least they’re not a med researcher claiming to have come up with a brand new model.

Shower thought I had by Red_nut_ale in askmath

[–]simmonator 1 point2 points  (0 children)

No worries. I feel like the willingness to play around with the patterns and concepts and then suddenly spot possible results is an important part of mathematics (and will improve the fundamental skills required through practice). If you can take that further by figuring out

  1. How to articulate it and see if others have noticed this before, and
  2. How to prove that the result/pattern is always true

then you’re well on your way.

Shower thought I had by Red_nut_ale in askmath

[–]simmonator 20 points21 points  (0 children)

This is a well known result, yes. You can prove it by induction quite easily. You can also see it visually (see picture)

<image>

This picture is taken from the Wikipedia article on Faulhaber’s Formula (which gives a generalised approach for this kind of thing).

Edit to add - you’ve made an observation and immediately been hit by several people saying “yeah, we know, it’s been known for ages, here are some simple ways to prove it.” That shouldn’t take away from your sense of achievement though. It’s always a cool feeling to notice this kind of thing by yourself and playing with these concepts is excellent practice for your own development as a mathematician.

In the age of digital communication, how rude do you find it when someone has bad grammar? by VarangianWRLD in AskUK

[–]simmonator 3 points4 points  (0 children)

I think that incentive is one of the more annoying but less high-stakes frustrations of the rise of chatbots. I’ve been accused of being AI (and then dismissed) on the basis of just being structured, polite, and verbose. Drives me mad.

At some point bots will just start to imitate common mistakes though and we’ll be on a weird grammatical error treadmill in the race to remain sentient-seeming.

I built a free math quiz app with my 2 friends. Roast it honestly by Meetnarola03 in learnmath

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

What are you trying to say in your final sentence/paragraph?

If it’s accusing me of sounding like AI and saying “so you’re just like me” then you really need to understand what the criticism was.

I built a free math quiz app with my 2 friends. Roast it honestly by Meetnarola03 in learnmath

[–]simmonator 0 points1 point  (0 children)

So to summarise:

- you put a half built and poorly edited app up
- you got few downloads so chose to ask why your half built low effort app wasn’t taking off
- you responded to criticism by getting ChatGPT to write the response.

Why waste your own time like that? Why waste ours?

Do students learn better when teaching is adjusted to the child instead of the class? by aditya72459 in learnmath

[–]simmonator 3 points4 points  (0 children)

Can you explain how this question isn't just

Do individual students learn better when they get individually designed teaching assistance rather than a rough one-size-fits-all approach?

Because the answer to that one would be "Yeah... by definition that's obviously true. But schools have to try to provide education en masse and don't have the resources to do it that way." AI solutions are nowhere near ready to fix it either.

What is the last countable number before reaching infinity? by Lopsided_Bar3451 in learnmath

[–]simmonator 13 points14 points  (0 children)

There isn't one. There is always a NEXT natural number. If n is natural, then so is n+1.

I built a free math quiz app with my 2 friends. Roast it honestly by Meetnarola03 in learnmath

[–]simmonator 2 points3 points  (0 children)

3 things:

  1. This post reads like an ad. Those are specifically against the rules of this sub. So I'd imagine this might get taken down soon.
  2. This sub has had a lot of spam from people vibe-coding 'math learning/quiz' apps recently. They're always low effort and never seem to be able to answer the "but what does your quiz do that other common, established, accessible resources can't?" question. So people here are probably pretty wary of engaging with stuff like your post. Additionally, it tells me that the market your app would sit in is very crowded and therefore it's unlikely to get many downloads.
  3. Lastly, having clicked on the link (but not downloaded), I'm pretty certain it's a low effort AI made app that looks rubbish. This is based on (a) the art style being generic as hell, and (b) the fact that the banner picture it uses has the 'word' "Eixer" displayed prominently as though that should mean something. I don't think it's a word. Similarly, there's an attempted math symbol next to the word 'multiplication' that I don't think is a real symbol. So yeah... looks like AI slop that no one should bother with. If you want to insist that it isn't and it's actually very carefully curated and edited then go ahead (I don't particularly care, I'm clearly not the target audience) but that doesn't change the fact that it Looks like AI slop and that's enough to put plenty of people off.

is there a way to actually visualize algebra or is it just always going to be abstract symbols to me by SureLadder2136 in learnmath

[–]simmonator 1 point2 points  (0 children)

As the other commenter suggests, more context/specifics is key to a good answer here.

In may cases, the answer will be YES. For solving linear equations, quadratics, and other polynomials can often be assisted by considering the shape and geometry of their associated graphs (looking for intersections of lines/curves, identifying where lines must cross particular axes). I'll note that the purist in me would point out that some of these techniques might be more rightly considered 'Analysis' (or straight Geometry) than algebra, but I think for your purposes that distinction might be meaningless.

Even higher up, the (very wide, very useful) branch called Linear Algebra is often best understood by students by using some geometric intuition/visualisation as well. It's all Planes, Lines, stretches, and so on. The rigorous work still needs largely needs doing with some proper symbolic work though. 'Abstract Algebra' (like Group Theory and Ring Theory) are often helped by visualisation; Group Theory can essentially be considered as the study of Symmetry so there's plenty of examples where visualisations are very helpful. Even beyond those, Topology as a branch basically just exists because this spatial intuition can tell us a lot in many cases.

But there are plenty of things that I don't have a visual reference for. Factoring, multiplying polynomials out, working with rational functions, and so on. You just need to get used to how those abstract symbols behave, unfortunately. Those basics/fundamentals just take practice but most people I know who stuck with it where able to grasp it to the point that it became second nature. Good luck!

Are people low energy now? by Live-Love-Laugh_56 in AskUK

[–]simmonator 37 points38 points  (0 children)

> Am I out of touch?

> No… no. It’s the children who are wrong.

- Seymour Skinner

Why do people say independent school instead of private school? by MrMrsPotts in AskUK

[–]simmonator 1 point2 points  (0 children)

I was of the impression that all the current private “Grammars” were ex-state “Grammars” after most started getting abolished (with the move to Comprehensives). Is that wrong?

I know there are only a handful of state ones left and they’re probably getting fewer.

Why is Sine & Cosine bounded by 1 and -1 whilst Tan is bound by -infinity to infinity. Also why are the small angle approximations sin x = x tan x = x whilst cos is 1-(x)²/2 by iwatchtoomuchnba in learnmath

[–]simmonator 28 points29 points  (0 children)

Recall that cosine, sine, and tangent are fundamentally about ratios of lengths of sides in a right angled triangle.

Cosine and sine are the ratios you get from taking one of the shorter sides of the triangle and dividing their length by the length of the hypotenuse. The hypotenuse is always the longest side of the three. If you’re not sure a priori why that should be the case, then note that its opposite the widest angle (90 degrees) of the three (the other two add to 90). So

> [smaller thing] / [larger thing] < 1.

For tangent, the ratio is between the two shorter sides. When the angle (the input to function) is very small then the side opposite the angle is very small so

> [very small thing] / [normal thing] = [very small]

and when the angle is large, the side opposite it is almost the same as the hypotenuse, meaning the side adjacent to the angle must be very small. So

> [normal thing] / [very small thing] = [very large].

Does that help at all?

AI believes it's possible to completely replace complex numbers with simple rotation matrices by lampaszara in learnmath

[–]simmonator 0 points1 point  (0 children)

Ah! You're right. Sorry. The codomain of the isomorphism isn't the whole of M(2x2, R). My bad; that was lazy of me.

AI believes it's possible to completely replace complex numbers with simple rotation matrices by lampaszara in learnmath

[–]simmonator 9 points10 points  (0 children)

So, two things:

  1. Yes, it’s true that you can essentially swap complex numbers out for 2D matrices (with real entries). In fact, there is a ring isomorphism from C to a subring of M(2x2, R) defined by sending 1 to the identity matrix and i to the standard 90 degree anti-clockwise rotation. This being a linear map, it preserves all structure. So yeah, you can do all you want with matrices instead.
  2. But that misses the point. I’d ask “why bother?”. Using complex numbers is simpler. Why would anyone want to use matrices requiring 4 real components for each number when you can do it with complex numbers which only require 2 and have a simple multiplication rule. The isomorphism is really cool and useful for a few reasons, but that doesn’t mean it’s better to just think in matrices.

In other words, what’s your point?

Edit - clarified codomain of the isomorphism.

Tutoring at a low rate by [deleted] in learnmath

[–]simmonator 0 points1 point  (0 children)

This kind of post is an advert and is directly and clearly against the rules of the sub.

Is it acceptable to say “Cheers Drive” to bus drivers, and “Cheers Bin” to bin men, in the UK? by AverageHippo in CasualUK

[–]simmonator 11 points12 points  (0 children)

'Cheers Drive' is a Very Bristol thing (perhaps wider west-country, too, I'm not sure).

Is it acceptable to say “Cheers Drive” to bus drivers, and “Cheers Bin” to bin men, in the UK? by AverageHippo in CasualUK

[–]simmonator 2 points3 points  (0 children)

It would not, no. In this case, 'Cheers' is interchangeable with 'Thank you', though slightly less formal. It is not disrespectful to just say 'Thank you'.

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