Formulas

[CzarJ]

Perhaps it would be best if we had a place where we could put all the formulas we can think of (whoa, long list). I'll start:

GEOMETRIC AND FERMAT'S LAST THEOREM

code:

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square: A=L^2


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rectangle: A=LW (perimeter: P=2L+2W)


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circle: A=pi*r^2 (circumference: C=pi*d)


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triangle: A=(1/2)*b*h


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trapezoid: (1/2)*h(b1+b2)


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surface area of sphere: S=4*pi*r^2


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volume of sphere: (4/3)*pi*r^3


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cube:V=s^3


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rectangular prism: V=LWH


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cylinder: V=pi*h*r^2


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pyramid: (1/3)bh


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Pythagorean Theorem: a^2+b^2=c^2


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Fermat's Last Theorem: x^3+y^3=z^3

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Ok,ok, I have no idea what that last one is, and it probably has nothing to do with area.

Algebraic

code:

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Slope Formula: m=(y2-y1)/(x2-x1),where m is the slope and


(x1,y1) and (x2,y2) are coordinates for 2 points on a plane.


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Quadratic Formula: if ax^2+bx+c=0,x=(-b±sqrt(b^2-4ac))/2a


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Distance between two points: d=sqrt((x2-x1)^2+(y2-y1)^2), where


(x1,y1) and (x2,y2) are coordinates for 2 points on a plane.


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Midpoint Formula: The midpoint between (x1,y1) and (x2,y2) is


(((x1+x2)/2),((y1+y2)/2))

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PROBABILITY

code:

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The probability of any given outcome in 2 related events is P(x)*P(y)


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Binomial(n,k)=(n!)/(k!*(n-k)!)

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Please tell me where I screwed up and feel free to add others.

[This message has been edited by CzarJ (edited 05-22-2001).]

[AcidFast]

If you would like to know more about Fermat's Last Theorem (or FLT for short...), you can check it out [url=http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Fermat's_last_theorem.html]here[/url].

Its actually a very interesting little story.

[This message has been edited by AcidFast (edited 02-29-2000).]

[Amy]

For even more wild fun, we should try deriving these ourselves.

[araya]

I was waiting for somebody else to notice, but that pyramid equation is a bit fishy

[Ghost Post]

I think the pyramid formula is right.

V = 1/3 * B * h, where B= Area of the base.

I believe this is true regardless of the shape of the base. So, a cone's volume is:

V = 1/3 * (Pi * r^2) * h

If the base is a square, you'll get:

V = 1/3 * (s^2) * h

Somebody correct me if I'm mistaken.

[araya]

oh yeah, that is right.. looking at the equation, it looked like an area equation (dimensional analysis). It wasn't clear that b was an area measure.

[CzarJ]

A few corrections:
Fermat's last theorem: x^n+y^n=z^n
The name of this thread should be "Formulae"

and an addition:
Falling Object Model: h=-16t^2+s, where h is the height at time t when dropped from original height s.

[araya]

Fermat's last theorem is that there are no integer solutions for x^n + y^n = z^n for n > 2.

What are the units on your falling object equation?

[CrystyB]

for the falling object: PLEASE say in what units you measure the acceleration. I am used to 9.80665 m/(s^2), so we would have h=s-5(t^2).

And you have been in a little hurry when typuing the distance between two points and forgot the second "square" (or at least its exponent).

What about TRIG? Never heard of sin(sum)=sincos+sincos, cos(sum)=coscos-sinsin? And all the other hundreds of formulAE?

[Quailman]

Objects fall at a different rate in the US than they do elsewhere. That's 32 feet per second^2.

[CzarJ]

sorry about the falling object thing. I don't know anything about trig, so I'll have to rely on the rest of you to help me out there. This wasn't intended to be just me typing everything I could think of.
h=-16t^2+s where h=height in feet at time t in seconds, dropped from an initial height (in feet) of s.

[godeloo]

x^2+y^2=Z^2
This formula has an infinite number of whole number solutions.
If you want some just ask

[mithrandir]

that's why n > 2

[CrystyB]

godeloo, please tell me some more pythagorean numbers besides the all-known n, (n^2-1)/2 and (n^2+1)/2, for any n which is an odd (i mean 2k+1, i never knew what odd/even are for) positive integer.

P.S. CJ, i usually don't like repeating myself, but you might not have heard: you're missing a "^2" in the distance formula. And the last two of "Area & Volume" should be in "Theoremes" or something.

edited on 06-08, 06-20 and:

[This message has been edited by CrystyB (edited 08-14-2000).]

[mathgrant]

Bump.

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"Mathematics is like the Nile, begins in minuteness, ends in magnificence." --Charles Caleb Colton

[Ghost Post]

Do you want to keep this isolated to math and calc formulas (abstract stuff), or should I dig up all my (concrete) physics formulas too?

[CzarJ]

Have at it!

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Basket-Weaving For Donuts, Where You Weave Baskets And Get Donuts.

[mole]

The probability of a given outcome in two related events is (Depending on the events)

P(x) * P(y|x)

Not sure about the notation, but that's meant to say "the probability of y provided x happens"

YOu shouldn't have to worry about it most of the time (flipping coins is a good example), but the extra factor is important when dealing cards, or other things that change the situation when the event occurs.

[Ghost Post]

Well, I started typing out physics formulas, but I realized that a large portion of them either use special unicode characters only visible to users of windows 2000 (such as delta, gamma, and mu), or they use subscripts and superscripts which can't be expressed in UBB, or both. I decided instead to simply scan in my formula sheet . It is now posted at http://www.mnefstead.f2s.com/images/phys11.gif
When I have my physics 12 formula sheet handy, I'll scan that too. Cheers!

[This message has been edited by ThePoet (edited 05-26-2001).]

[Ductape]

Hero's formula

A^2=(s(s-a)(s-b)(s-c))
s=1/2 (a+b+c)

i think this is for area of a triangle

[CrystyB]

Why did you bumped it? There is the possibility of "Show all topics..."

And btw, the distance between two points in space is sqrt((x1-y1)^2+(x2-y2)^2+(x3-y3)^2)

[This message has been edited by CrystyB (edited 07-30-2001).]

[mole]

Or should that be sqrt((x2-x1)^2+(y2-y2)^2+(z2-z1)^2)?

[Ghost Post]

How about PV=nRT... etc etc etc... or does chemistry not count?

[CrystyB]

I subsribe to PV=nRT !!! Please add a chemistry section... I LOVE chemistry.

Ow, i mean i lovED chemistry. I can only think of concentration formulae right now:
In a water-solution of a substance,
the mass concentration is (100*m_subst/m_solution)%
the volum(etr)ic concentration is (100*V_subst/V_solution)%
the molar concentration is (m_subst/MM_subst)/V_solution[in liters]
(MM means molecular mass)
the normal concentration is molar_concentration/nb_electrons_"used"
(eg: that number is 1 if HCl, 2 if Na2SO4, 3 if AlPO4 and so on)

[This message has been edited by CrystyB (edited 07-30-2001).]