Math Is Fun Forum

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

squares just above one

This is really simple, but
neat to me.
1.01^2 is 1.0201
But that is also
0.01 x 2.01 + 1.

This is analagous to:
8^2 = 64
But also
(8-1) x (8+1) + 1 = 64 too.

So 1.001234^2 =
0.001234 tmz 2.001234 plus 1.

Silly, I know, but inspirational too!!

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igloo myrtilles fourmis

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: squares just above one

I always knew that the decimal part just more than doubled, but
know I can see just how much more than doubling it doubles.

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igloo myrtilles fourmis

esatpllana

Member

Registered: 2007-11-22

Posts: 12

Re: squares just above one

wow very nice I tried with other number
that's great

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John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: squares just above one

Yeah, I love little finds like this.  It's like building a puzzle of knowledge.

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paulienom

Member

Registered: 2008-03-24

Posts: 0

Re: squares just above one

What does E=MC2 mean?

luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

Re: squares just above one

E = mc²  is an equation that shows the equivalence of mass and energy derived by Albert Einstein.

But why did you ask this in this thread?

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John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: squares just above one

E is energy
m is mass or weight sort of, but weight without the gravity.
c is the fast speed of light or slow speed of light depending on if you human or on star trek.
c² is the light speed multiplied by the speed of light onto itself.

The binding energy in atoms lowers the "weight", oh, I mean "mass".
I think the binding energy might hold the neutral neutrons and the
repelling protons all together at the center of the atom.  When you
learn about isotopes in chemistry, try averaging the masses or
atomic weights for one thing like iron or gold or tin, but if it is off,
maybe your percentages are not accurate or maybe the binding
energies must be converted to Less Weight or Mass.

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igloo myrtilles fourmis

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: squares just above one

I think the binding energy might hold the neutral neutrons and the
repelling protons all together at the center of the atom.

That's the strong force.

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

simron

Real Member

Registered: 2006-10-07

Posts: 237

Re: squares just above one

I know how this works.

P.S. What does Q.E.D. stand for?

Last edited by simron (2008-05-10 04:33:57)

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JohnnyReinB

Member

Registered: 2007-10-08

Posts: 453

Re: squares just above one

Let me get it straight

(a-1)(a+1)+1 = a^2+a-a-1+1 = a^2

Did you know that (a-b)(a+b) is a special product? It always is (a^2)-(b^2)

So, the one above can be simplified into

(a-1)(a+1)+1 = (a^2)-1+1 = a^2

Pretty neat, isn't it? Independently discovering a key to Special Products!

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luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

Re: squares just above one

Q.E.D. stand for?

It's latin, standing for: quod erat demonstrandum - literally translated as 'that which was to be demonstrated'

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