How many Kenneth’s are in one Ken?
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How many Kenneth’s are in one Ken?
Hello! for the longest time I've thought that I'm just "not good" at math, and that I'm just a creative type or something, but for the past few years I've been trying to brute-force my way through math drills and stuff to improve because I want to go into a STEM field. I've found that it doesn't work. I have, however, gained a kind of Stockholm syndrome for math, and I find myself wanting to know *more*. I feel like I'm missing out on something way beyond myself but idk where to even find that. So here i am. Asking a blog on tumblr for the secret math knowledge. If you have any resources that i could read about math that isn't just "here's how to do this" i would really appreciate it!!!
First of all, complete props to you for giving something that doesn't initially appeal to you, in this case, maths, a chance. Mathematics can be frustrating and even annoying, being an oftentimes nit-picky field. You can quickly realize that these are also the traits that grant the satisfaction and euphoria of mathematics. So don't forget to be proud of yourself for not disregarding mathematics as a whole and actually giving it a go.
Second of all, creativity is very necessary for maths. It is a shame that the educational system doesn't do maths justice (A Mathematician's Lament by Paul Lockhart is exactly about this). Mathematics is presented as something mechanical, force-feeding formulas and having students repeat them to find adequate results. That is not a fair portrayal of mathematics.
Different people will have different conceptions of what the learning of mathematics is or should be - I mean, for god's sake, mathematics hasn't even been defined properly and one expects people to know what to do with it. I can only tell you what I conceptualize mathematics, and its learning, to be. For me, mathematics is the boring work of examining multiple results and cases of the same formulas, it is the finding of patterns and attempting generalizations, it's the excited scribbles of formulas and the necessity of looking at a particular scenario from multiple perspectives. Most likely, the generalizations won't come easily, a minus sign will be forgotten making the following calculations obsolete, an approach to a problem will prove fruitless, and laborious work will be done only to find out there was a specific theorem that would have shortened the whole process. Patience is required for maths, and hopefully, you can now see that creativity is too, there is no shortcut to knowing where to look or what technique to utilize. As is the case with most worthwhile pursuits, and as you know from experience, mathematics is endlessly frustrating, but that also means it is endlessly fun.
Now, I do not have any secret math knowledge (or do I), what I can do is present you with some things that fascinate me and have led me to love mathematics as much as I do, outside of the conventional mathematics curriculum.
Maths really comes down to practice, practice, practice... as many other things. I heavily encourage you to start playing around with mathematics a little bit. Olympiad mathematics kind of do that, (I, very conveniently, have a lot of posts about that.) as do many other math competitions. Maybe try out some exercises from your national olympiad and, with no judgment, because this is just to have fun, play around a bit. Disregarding the conventional maths you know, test out your logic, laugh at mistakes and losses of time, and feel that happy rush when a conjecture you reach, or part of it, is correct.
In terms of the resources, I opted for a mix of funny math history moments and some actual mathematics, in no particular order. Prepare for confusion. ↓
This is a simple way to get product of 9 and any integer between 0 to 10
File photo of me getting stuck doing stupid shit.
Like maths 😶
On the WURSTKATASTROPHE and hairy spherical cows
For the non-German speaking people: The word in the title literally translates to SAUSAGE CATASTROPHE.
You may ask yourself "huh?" and you would be right to do so.
Today I was browsing Wikipedia for some maths stuff. Then the magic of Wiki happened and I clicked one of the many links flying around. I landed on the page for half-integers. These are somehow related to the problem of packing 4-dimensional spheres as tightly as possible (the least amount of space wasted). I read something about that stuff before, so I searched for links leading me to the German page about packing a finite amount of spheres. https://de.wikipedia.org/wiki/Theorie_der_endlichen_Kugelpackungen
This is where the WURSTKATASTROPHE comes into play. If you would like to pack a number of spheres (say, oranges or so) with as little wasted space as possible, what would you do?
Well, the theory of finite sphere packing will tell you, that the form of a sausage would be best (you line them up), BUT this will only work until the WURSTKATASTROPHE takes place. Starting with 55 spheres, the sausage form won't be the best anymore, instead some sort of clustering would fit better. Man, what a disaster!
But don't despair, for there is the WURSTVERMUTUNG (literally sausage conjecture). If you were to live in a higher dimensional plane (starting with 5D), the sausage form would always be best. Sadly, this isn't proved yet.
There are some kinda weird things in maths. I will now explain the second part of the title.
Let's start with the weird thing. The hairy ball theorem ( https://en.wikipedia.org/wiki/Hairy_ball_theorem) . It states (paraphrased), that if you had a ball full of hair, you wouldn't be able to comb it in such a way, that no hair would stand up. In other words: There would always be a cowlick.
What can you do with that. Well, you can model some realistic real life scenarious. Let's assume you had a perfectly spherical cow (https://en.wikipedia.org/wiki/Spherical_cow), just as you can see running around on the fields. You are asked by friends to show it to them, since they like cows. Of course you want to show its best side! So you comb it, but oh noes! Your cow will get a cowlick and there is nothing you can do about that!
Knowing the maths could have prevented you from doing all the pointless work!
It's fun reading about weird mathy things and there are quite a few :)