Math nerds!

[MadMojoMonkey]

Here's a fascinating shortcut to squaring numbers that end in 5.

25^2 = (2*3*100) + 25 = 625

75^2 = (7*8*100) + 25 = 5,625

105^2 = (10*11*100) + 25 = 11,025

See the pattern? I never saw this correlation to numbers that end in .5

3.5^2 = 3*4 + .25 = 12.25

5.5^2 = 5*6 + .25 = 30.25

Someone was griping about an inability to calculate a square root and I realized there is a quick way to estimate 1/2 integer squares. It correlates to 1/4 integer squares, but the multiplicands become pretty large.

2.25^2 = 22*23/100 + 0.0025 = 5.0625


So something like
C*10^Z + 5*10^(Z - 1) has a shortcut

C*10^Z + 5*10^(Z - 1)
= C^2*10^(2Z) + 10*C*10^(2Z-1) + 25*10^(2Z-2)
= C^2*10^(2Z) + C*10^(2Z) + 25*10^(2Z-2)
= ( C^2 + C + 25*10^(-2) )*10^(2Z)
=( (C)(C + 1) + .25 )*10^(2Z)

It's a proof, but the shortcuts are so easy to remember.

[bigred]

Or you could use a calculator

[Savy]

Or you could use a calculator

If you've got a maths related degree you are a calculator.

[bigred]

Probably not as good as a machine and obsolete. Hail our future robot overlords.

[wufwugy]

If you've got a maths related degree you are a calculator.

the sad thing is with all the time we waste on learning how to long hand shit, i feel like i could learn all application skills necessary for several math-based fields.

no i dont need to know how to find root 7 without a calculator. maybe the government should stop subsidizing philosophy institutions so we can finally stop over-educating everybody.

[spoonitnow]

I had a big thread with a lot of stuff like this a while back: Simple math you DON'T need to know

It doesn't look like the shortcut links in the OP still work, but they're all in that thread.

[MadMojoMonkey]

I do hold the opinion that the education system is way behind the times as far as acknowledging the ubiquity of computers and calculators.

The thing that a computer can not do is choose the correct equation to solve. Once given the correct equation, though, it will solve it remarkably quickly.

The human advantage is in knowing what equation you want to solve.

I feel like a huge portion of my math education focused on how to solve the equations and not how to ensure I am solving the correct equations.

It's good that some group of experts understand how to create and program those computers. I'm just not sure where to draw the line at what minimum level of math provides the most benefit to society for a reasonable cost (intentionally ambiguous).

[spoonitnow]

On a related topic, there's a situation in chess right now where the combination of a strong computer + player is much stronger than either by itself. Computers are really good at looking at individual moves and variations (much better than humans to say the least), but they're not nearly as good at finding the moves and ideas to investigate initially as humans are.

[MadMojoMonkey]

Also, I am faster than a human using a calculator using the shortcut in the OP for numbers from 5 - 105.

They all end in 25. Ignore the last digit (5) and multiply the rest by itself plus 1. Drop it in front of the 25.

In my head it's just this
25^2 = (3*2 = 6) 625

It's faster than typing it in to a calculator.

This all started as I was thinking of a way to estimate a square root in your head. The guy postulated that calculating sqrt(57) without a calculator could be a necessary life skill. (OK, whatever... hard to imagine, but OK)
I thought, well, I know
7 < sqrt(57) < 8

cause obv.

How close is 7.5?
well, 75^2 = 5625
move the decimal and 7.5^2 = 56.25

A decent estimate for sqrt(57) is ~7.5. Maybe 7.6-ish

So the lack of calculator probably doesn't cost me too much. I got 2 sig-figs in ~5 seconds with a little mental number juggling.

EDIT: without knowing how to calculate a square root by hand.

[wufwugy]

I do hold the opinion that the education system is way behind the times as far as acknowledging the ubiquity of computers and calculators.

The thing that a computer can not do is choose the correct equation to solve. Once given the correct equation, though, it will solve it remarkably quickly.

The human advantage is in knowing what equation you want to solve.

I feel like a huge portion of my math education focused on how to solve the equations and not how to ensure I am solving the correct equations.

fucking. exactly.

[spoonitnow]

I think that learning how to solve those equations (following the example) on a highly-detailed level is important for developing the intuition needed to know when to use them. With that having been said, the lack of focus on using that intuition and realizing that you're building it in the first place is ridiculously bad.

Doing tons of trig identities is a good example.

[vatopkr]

Nice tip, How can use it when i am playing poker? heheh
This tip is very useful

[MadMojoMonkey]

Nice tip, How can use it when i am playing poker? heheh
This tip is very useful

I can't think of any applications to poker, really.

The only time I recall using a square root in poker is when thinking about defending the blinds. This isn't something that I would really bother with at the table, just something I'd study to make a plan.

This is the Community Forum, though, and we don't talk poker in this forum.

[jackvance]

On a related topic, there's a situation in chess right now where the combination of a strong computer + player is much stronger than either by itself. Computers are really good at looking at individual moves and variations (much better than humans to say the least), but they're not nearly as good at finding the moves and ideas to investigate initially as humans are.

Computers have been better than people in chess for many years now, quite frankly it has killed the sport. Like, computers are better across the whole board, there's no middle ground where people excel anymore.