Should wizards be good at math? If not, who should be in a fantasy universe?

Should wizards be good at math? If not, who should be in a fantasy universe?

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Any tinkering race your setting has, such as Gnomes or Dwarves, should definitely be good at math and geometry. Wizards, who rely on magic, should only need basic addition/subtraction skills, more or less so depending on if magic is "Vancian" or not.

Wizardry is typically a "science" in fictional settings, with specific measurements and calculations going into spells, so by all means they should have a solid understanding of mathematics. Doubly so if magic is interlinked with other sciences like astronomy or chemistry.

>'you should be able to do this'
>not 'you should be able to solve this'
You're letting Kuro-sensei down, OP.

In my settings, wizards are anal linguists rather than mathemagicians. Math has its place, but other things are more important. If your handwriting doesn't look computer-printed and you can't draw a perfect circle with your off hand, better forget about being a wizard.

1. Exactly one. You can define a triangle completely by providing exactly three values (out of six possible) of either inner angles or side lengths of said triangle.
2. I don't give enough shits to actually bother with it, but the cosine theorem (a.k.a. extended Pythagoras theorem) provides the solution.
3. Again, cosine theorem.
4. Draw a height from (a,b) to the x axis. You now have two right-angled triangles with known angles and one of the sides for each. A side of one of those provides the x coordinate, while a side of the other provides the y coordinate of the (a,b).

No

Whoever studies math

a = 130.

I've been purposely avoiding posting here, but you use the law of sines to determine the angles and lengths of sides. Next you drop a perpendicular to determine the a and b coordinates using the Pythagorean theorem.

1. Wrong. That only works if the angle sits inside the lengths, or vice versa. If you imagine drawing an isosceles triangle with a base that's part of (0,0)->(a,b) and with one side being the line of length 7, then you can also see that the isosceles triangle's other side is also a line of length 7 that connects the fixed point at the end of the line of length 5 to the unknown length.

2) Top Angle = asin( 7/5 sin56 )
Incidentally, that gives two values, because sin(x)=sin(180-x), but your calculator might not tell you that. Work backwards and you'll see.
3) Calculate the top angle, derive the bottom-right angle because of angle sum, then use the sine rule again
4) Trigonometry again. Sin(56)*Top-right-line gives b, then Cos(56)*Top-right-line gives a.

Who knew a flair for numbers was a shortcut to 30 years of virginity?

Your 1 is so wrong it hurts.
Think of the '7' side as the radius of a circle, center on the intersection of '5' and '7'. The circle will hit the third side on 2 points, or, if tangent, on a double point (but that's not the case because of pyth. theorem: you'd need a right angle on the (a,b) vertex, pythagoras theorem immediately shows it's impossible).

...

Can someone else check this math? I can't help but think it's off, though it might just be the diagram itself that was used

I was on the same track, but got annoyed with how off the picture was and gave up before getting to like half of those numbers

It looks legit. The diagram is off.

they would be good at math, maybe not phenomenally, but wizard magic is generally done through precise and careful study, this would give a leaning towards being well-studied and place an emphasis on logical reasoning, so even if wizardry doesnt require advanced math, its practitioners would definitely lean towards being math savvy

>remembering spells
>alchemy
No. Being "good at math" I'll say is having a master's degree. These wizards know basic geometry and arithmetic, and maybe some algebra. I'd be surprised if they even accepted the existence of irrational numbers.

We're not sure any numbers exist.

>what is the square root of two
I don't know what reality you inhabit, but it is not the real world.

Number is an abstract concept. Does it exist in real world? What is it's mass? Where does it reside?

1. Two solutions for both unknown angles.
2. Not bothering now
3. There are two answers.
4. There are two answers.

imo doing wizard shit should require something similar to hardcore pure mathematics

Depends on how magic works. If it's just straight up evocation, then no. If it's a science alongside metaphysics and alchemy and other pre-modern doctrines, then yeah, probably.

I prefer settings where magic is more sciencey just because it keeps better internal consistency (if I can sling a fireball, why can't I light a cigarette?) so I'd prefer wizards be more academic.

>I'd be surprised if they even accepted the existence of irrational numbers.

>yfw the Lightning school has but the other elemental schools haven't because manipulating electricity requires complex and irrational numbers but human-scale engineering largely doesn't

Alternating current requires some irrational numbers. You can workwith direct current with quite simple math just fine, and most natural electrical phenomena, including lightning, are direct current.

Obviously irrational numbers are a large part of Dark Arts.

You can be academic without being a scientific.

I don't like wizards being good at maths or science in general, because it forces the magic=fantasy science

I prefer my magic as an occult art, full of mystery, symbology, weird incantations and lots of fuck up.

I prefer a scholar, well versed in languages, history, spirits, etc. than a scientific.

duckware.com/tech/worldshardesteasygeometryproblem.html

1. Calculate some known angles:

ACB = 180-(10+70)-(60+20) = 20°
AEB = 180-70-(60+20) = 30°

2. Draw a line from point D parallel to AB, labeling the intersection with BC as a new point F and conclude:

DCF ACB
CFD = CBA = 60+20 = 80°
DFB = 180-80 = 100°
CDF = CAB = 70+10 = 80°
ADF = 180-80 = 100°
BDF = 180-100-20 = 60°

3. Draw a line FA labeling the intersection with DB as a new point G and conclude:

ADF BFD
AFD = BDF = 60°
DGF = 180-60-60 = 60° = AGB
GAB = 180-60-60 = 60°
DFG (with all angles 60°) is equilateral
AGB (with all angles 60°) is equilateral

4. CFA with two 20° angles is isosceles, so FC = FA

5. Draw a line CG, which bisects ACB and conclude:

ACG CAE
FC-CE = FA-AG = FE = FG
FG = FD, so FE = FD

6. With two equal sides, DFE is isosceles and conclude:

DEF = 30+x = (180-80)/2 = 50

Answer: x = 20°

Forgot to add the complementary image.

You know, the thing that bothers me most about this, besides the fact that I can't arse myself to solve this problem so I can look good on an anonymous imageboard, is the fact that the side labeled '5' appears longer than the side labeled '7'.

Yeah but the old school Pythagoras cult kind of math.
About half of it is proper math, even amazing math, the other half is calculating how many angels can dance on the head of a pin and the vectors on which love travels. Learning the moods and politics of the numbers themselves and the proper seasons and colours in which to write equations.

Somewhere between the practical and ridiculous, magic happens.

Of course math isn't the only academia wizards butcher. Proper wizards deal in biology, history, art and cooking and all number of esoteric crafts.

>the side labeled '5' appears longer than the side labeled '7'.

That's done on purpose for a lot of geometry and trigonometry problems, precisely so you don't try to "trust the diagram" and just measure it or whatever.

I know, and I figured someone would mention that, but it still triggers my autism.
Besides, for the sake of a math problem, simply measuring it doesn't count as proving that it's actually that length, so I don't see why anyone would do it anyways.

Honestly, that's all the math that was discovered before Descartes. If a wizard knew all that, he'd be the best in the world.

>Should wizards be good at math?
If they're also assumed to be alchemists, yes.
If you mean just for spellcasting in itself it depends on how magic is conceived of in a setting.

Generally, per D&D definitions of things as I understand them, yes, math is important. The finer points of bog-standard arcane spellcasting is built on ideas of Plato's geometric esotericism and the Greek classical elements, where elements are derived from and made up of their pure platonic forms which also exist primarily on a plane of pure information.
Spellcasting in this ethos works by poking and prodding at that barrier using a combination of will and being able to hold perfect expressions of that geometry, simultaneously as a visualization and a cluster of mathematical expressions, in your mind. The better a wizard you are, the better you can do this and the less energy and focus it can take to do it.

As for bards, it can vary whether stories and music have a pure sort of magic in them all their own (if you can only express them perfectly enough), or it's the mathematics of musical theory which is extended as well to to the art of constructing stories.

This, and I would add alchemists to the mix as well as just mixing a bunch of shit together is a good way to get blown up and/or melt off your face.

>who should be good at math in a fantasy universe?

Engineers, mathematicians, merchants, moneylenders, treasurers, navigators, and polymaths.

>tfw you somehow thought going mechatronics was a good idea despite your shitty math
Should have just go do paramedic and then blame father if I couldn't find the job in this because he strongly recommended it.

But your field sounds so cool though.

>So what do you do, user?
>I'm a mechatronics engineer
>You just made that up user, what do you actually do
>I'm serious! It's called mechatronics
>So what, you repair giant robots?
>...kinda

>>panphysicalist can't into basic math.
>>nobody is surprised by this, obviously.
Pi.

Your ABC triangle has a total of 190* of angles. 90+80+20

It's a mix of mechanics, programming, electronics and automatics, more or less.

A lot of math, physics and mechanics I know jack shit about(I barelly passed math in highschool due to laziness).

I seen mechatronics as fun degree where I get to build robots and shit. I believed that my laziness is just temporary, so I will learn what is needed, while I find myself job to pay it off myself (college in weekend system).
Fucking nope, I fell quite behind already in highschool and now it's quite a nightmare. Either somehow I drive myself insane and somehow pass the tests and I will be shitted on by parents for dropping out.
I feel so hopeles that I didn't even try to learn through all that summertime I had, fucking hell.

>Should wizards be good at math?
Probably better than most, but D&D-style magic seems a bit too... squishy and complicated to be *all* maths.
>If not, who should be in a fantasy universe?
These guys: and possibly also Mystics/Psions.

He got some things right, like the fact the central angle is divided in 130*,130*, 50* and 50*. We'll call the central point Y. What you know then is that you consider The triangle EDY (the one with the angle we're searching for, AED) and the angle BDC (that we know is 140* because BDA is 40* allright). And then
alpha= (140*-x)-130*; where (140-x) is BDC and x is BDE; so alpha= x-10.
Since you must get to 180* for the triangle BDY, you have 180*= 130*+(x-10)+x.
So 180*=120*+2x; 2x=60* and x= 30*.
So BDE is 30* and AED is 20*.
130+30+20 is 180 allright.
That's how I'd solved it without trigonometry and without drawing any lines.
Does well but probably got distracted drawing lines because the triangle ABC then has got 190* of angles.

>I feel so hopeles that I didn't even try to learn through all that summertime I had, fucking hell.

Nobody gets studying done during summer vacation.

BDC is 140, yes. You then set BDC to 140-x, instead of CDE.

Not necessarily.
They require int, but maybe the way they apply their intelligence to the study of magic doesn't help them with math.
Kinda think it would though.

And I'll toss this up as well.

You're right I inverted two angles.
Sorry Veeky Forums I failed you.