Volume of the sphere..............

[solo]

The long standing formula for the volume of a sphere is: [math]\left(r^3\right)*\left(\frac{4\pi}{3}\right)[/math] = volume of sphere

 

I have calculated a new and much simpler formula: [math]\left(\frac{dia^3 \pi}{6}\right)[/math] = volume of sphere

 

Anyone have something to add?..............solo

[Cap'n Refsmmat]

That's the same formula, simplified a tad.

[solo]

That's the same formula, simplified a tad.

Absolutely Cap'n........., simplified for the sake of convenience.....................solo

[Klaynos]

It's not much simpler, and nothing new in any way...

 

2Pir == Pid ya know...

[TriggerGrinn]

Thats cool.

 

I like expressing formulas in different ways.

 

Formulas are more than just math. They are a descrpition of objects and the relationship between things.

 

Kinetic energy:

 

[math] KE = \frac {1}{2}mv^2[/math]

>

[math] KE = \frac{(M*V) (M'*V)}{M + M'}[/math]

 

Kinetic energy that will be spent between two frames of mass that collide in 1d collisions.

 

M = Mass, and must be used as the lesser mass of the interaction. That is M and M' are equal values of mass in the equation but represent the lesser mass of two objects colliding, and when masses are equall the value can be used from either of course.

M = Moving object

M' = The object that the moving object collides with, (at rest)

V = velocity of object in motion relative to frame of reference at rest.

Equall masses convserve velocity and momentum in (perfect collisions) and experience the exact same force. value of force of -acceleration and value of foce for +acceleration F+F.

 

If two objects have different mass and collide, the force involved will only be as great as what the lesser mass can cause, with the considered velocity.

 

This equation :

[math] KE = \frac{(M*V) (M'*V)}{M + M'}[/math]

describes the energy spent between a simple 1d interaction between two objects of mass. For no object has energy without a partner frame to measure its velocity.

 

and of course this all can be expressed right into quantum behavior.

 

[math]\frac {1}{2}mv^2 = \frac {(m1 v) (m1' v)}{m1 + m1'} = \frac {p^2}{2m} = \frac {n^2 h^2}{8mL^2} = En [/math]

 

 

1. The energies are quantized and can be characterized by a quantum number n

2. The energy cannot be exactly zero.

3. The smaller the confinement, the larger the energy required.

[TriggerGrinn]

see the application of this equation at this link

 

http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/schr.html#c2

[solo]

It's not much simpler, and nothing new in any way...

 

2Pir == Pid ya know...

Actually, there is something new here. Examine the following formula:

 

[math]re=\frac{\left(\sqrt[4]{\frac{6}{\pi}}\right)\left({\sqrt[3]10}\right)^{25}}{c^2}[/math]............in cgs units

 

and;

 

[math]re=\frac{\left(\sqrt[4]{\frac{6}{\pi}}\right)\left({\sqrt[3]10}\right)^{7}}{c^2}[/math].............in SI units

 

Notice the involvement of [math]\left(\frac{6}{\pi}\right)[/math] within these formulae.

[Ragib]

What the hell is a? and what is i? If you mean the imaginary unit..how the hell does that come in...and its different, but not simpler or more convenient...you still have to cube a quantity..divide by a bigger number...i just dont get it.

 

Edit: O crap, this is in applied math section..my bad i thought it was pure math...

[uncool]

see the application of this equation at this link

 

http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/schr.html#c2

 

I looked, no sphere there at all. Please stop making plugs for your site.

[swansont]

I looked, no sphere there at all. Please stop making plugs for your site.

 

I think he was referring to the equations in his post. And I doubt hyperphysics is his site.

[Chainsaw Jim]

Since we mostly work in Radius rather than diameter I suggest 'four thirds pi r cubed' is the easier. it's the same number of components.

[Ragib]

I agree, just easier to stick to what's simpler.