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Offline AngelFish

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Cool math hacks
« on: May 05, 2011, 06:08:15 pm »
Have you ever taken a test (or just realized in general) that some of the methods taught in school are very tedious and there's a much faster way to do precisely the same thing? For example, one of the things taught in both Statistics and Linear algebra is finding a least squares regression line for a given data set.  Statistics teaches you how to solve:



while Linear algebra teaches you a very computationally intensive, often poorly explained method involving matrix operations.

While I was taking my Linear algebra final today, I realized that instead of solving those messes, the least squares regression line is actually a weighted "Average" of several other functions that depend on the values of the data set for the linear case, although it doesn't extend to higher order regressions. Thus, my answer took half a page to derive instead of the two pages given to solve the problem on and involved only very simple arithmetic to do the problem.

Has anyone else ever had a similar experience?
« Last Edit: May 05, 2011, 06:09:57 pm by Qwerty.55 »
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Offline ruler501

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Re: Cool math hacks
« Reply #1 on: May 05, 2011, 06:42:18 pm »
Kind of. I sit around in class all the time bored after I finish my books and usually I'll think about life, philosophy or math/science(same thing really in my opinion). I have found numerous ways to have easier solving of problems in class. Its just that most of what I figure out is proofs of what I already know or simplification of simple subjects(multiplication/algebra 1/etc). I'll post some of what I figured out later. most of it is published in one form or another and I come across them after I already came up with how to do it.

I'd kind of like to see your method for doing that

EDIT: some of what I did was prove parts of the Vedic Mathematics(Indian methods for efficient math solution) before I knew they existed.

I figured out their multiplication formula

(ax^2+bx+c)*(dx^2+ex+f)=x^4*a*d+x^3(a*e+d*b)+x^2*(b*e+a*f+d*c)+x(c*e+b*f)+c*f
This seems more complicated till you replace x with 10 and see how it is just place value if you flip the left side of the equation so that you go from least to greatest in powers you can do this quickly and accurately in your head.
This also proves that it will work with any base
« Last Edit: May 05, 2011, 08:41:22 pm by ruler501 »
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Offline Freyaday

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Re: Cool math hacks
« Reply #2 on: May 06, 2011, 11:58:19 am »
Yeah. This happens to me all the time.
Like, we were asked to find how far a ball drops in a given number of seconds, and we were supposed to use geometric sequences to do it, but using the little physics knowledge I have, I came up with something far simpler. t=time, a=accelleration, d=distance
dt=2t2/a
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Offline ruler501

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Re: Cool math hacks
« Reply #3 on: May 06, 2011, 01:23:46 pm »
Yeah schools teach the accepted methods only. My teachers complain whenever I use my own methods if i don't write out my entire proof which is sometimes only in my mind and is usually long

EDIT: changed excepted to accepted
« Last Edit: May 07, 2011, 07:43:58 pm by ruler501 »
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Offline jnesselr

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Re: Cool math hacks
« Reply #4 on: May 07, 2011, 03:50:57 pm »
Quote from: ruler501 on May 06, 2011, 01:23:46 pm
Yeah schools teach the accepted methods only. My teachers complain whenever I use my own methods if i don't write out my entire proof which is sometimes only in my mind and is usually long
Fixed, and yeah, I understand exactly what you mean.
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Offline Darl181

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Re: Cool math hacks
« Reply #5 on: May 07, 2011, 04:15:12 pm »
I forgot what it was, but at one point that happened to me. I asked the teacher to prove it wrong.  She never bothered me about that again XD

I have no idea what's going on in the first post tho...I've just seen the E looking thing before and idk what it's called :P
« Last Edit: May 07, 2011, 04:16:17 pm by Darl181 »
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Offline ruler501

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Re: Cool math hacks
« Reply #6 on: May 07, 2011, 07:45:58 pm »
Its a summation operator I believe.

I might be wrong here but I believe that is when you sum up all of the numbers in a series up to a certain point. The starting value is defined on the bottom and the ending value is on top.

I'm not sure what all that other stuff is though
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Offline Freyaday

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Re: Cool math hacks
« Reply #7 on: May 07, 2011, 07:46:49 pm »
The variable being changed is also defined on the bottom
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Re: Cool math hacks
« Reply #8 on: May 07, 2011, 07:57:25 pm »
you can hack math to do wonders.  Such as this:

1+(-1)

unoptimized version of 1-1 == 0.

I think this totally beats qwerty's example, but only by a little, but he did a great job with his kiddy-maths with differential regressions and conics and matrix algebraic solutions
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Offline ruler501

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Re: Cool math hacks
« Reply #9 on: May 07, 2011, 08:00:01 pm »
My math teacher has learned over time that questioning my methods when I get the right answer is not a good idea. Many of my proofs just serve to confuse him and go far above his level of teaching and knowledge. He knows I don't cheat by the fact I can prove everything I do(well 90+% of the time)

He got confused when I tried to explain why you use e^rt in population growth.
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Offline PeonHero

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Re: Cool math hacks
« Reply #10 on: May 07, 2011, 08:43:59 pm »
Here's a cool math hack:

Usually people are taught to do math arithmetic from right to left, but it's actually more efficient (easier and faster) to do it from left to right. Scott Flansburg aka "The Human Calculator" teaches children to do math from left to right and they end up able to do the majority of arithmetic problems in their head without even writing anything down. Try it.
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Offline ruler501

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Re: Cool math hacks
« Reply #11 on: May 07, 2011, 08:46:24 pm »
Could you explain how to do this different method of addition?
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Offline PeonHero

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Re: Cool math hacks
« Reply #12 on: May 07, 2011, 08:48:56 pm »
  55
+55
------

Normally you would carry the 5+5 on the right side first, which would be a 1, then add it to the 2 50's on the left, to make 110.

Doing it the left-to-right way, you just do 50+50 first, = 100, then 5+5 = 10, answer is 110
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Offline ruler501

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Re: Cool math hacks
« Reply #13 on: May 07, 2011, 08:52:16 pm »
but then you have to carry backwrds

  186
+145
-------

How would you solve that easier than the regular method
« Last Edit: May 07, 2011, 08:52:34 pm by ruler501 »
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Offline Xeda112358

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Re: Cool math hacks
« Reply #14 on: May 07, 2011, 08:57:16 pm »
Actually, the method from left to right is how I do it because I thought it was easier than what my teachers were teaching me! It feels smoother to me to do it that way.
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