Math Is Fun Forum

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Science laws and theorems

Cauchy–Schwarz inequality

     

All_Is_Number

Member

Registered: 2006-07-10

Posts: 258

Re: Science laws and theorems

Newton's laws of motion.

First law:- Every body continues in its state of rest or uniform motion unless compleeled by an external force to change its position.

Interestingly, this is not Newton's first law of motion. It is actually a restatement of his second law, F=ma.

Strangely enough, Newton made the oft repeated error when he stated the first law. However, in the pages of Principia immediately preceding his statement of the first law, he described the law as something substantially different.

The first law should be (and was described by Newton as):

There exists a frame of reference in which an object continues in its state of rest or uniform motion unless a net external force is applied to that object.

In fact, without this first law, the second law need not hold.

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You can shear a sheep many times but skin him only once.

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Science laws and theorems

The Sylow theorems (group theory)

1. If G is a group of order p[sup]n[/sup]k (where p is a prime, n and k are positive integers and p is coprime with k) then G has a subgroup of order p[sup]n[/sup], called a Sylow p-subgroup.

2. If P and Q are Sylow p-subgroups of G, there exists g ∊ G such that gPg[sup]−1[/sup] = Q.

3. The number of Sylow p-subgroups must divide the order of G and be congruent to 1 modulo p.

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Science laws and theorems

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Science laws and theorems

Planck’s radiation law

The intensity per unit wavelength

of the radiation of a black body of absolute temperature

is given by

[align=center]

[/align]
where

is Planck’s constant,

is the speed of light in a vacuum, and

is Boltzmann’s constant.

From this, both Stefan’s law (which states that the intensity of the radiation of a black body is proportional to the 4[sup]th[/sup] power of its absolute temperature) and Wien’s displacement law (which states that the maximum wavelength of the radiation of a black body is inversely proportional to its absolute temperature) can be derived.

To derive Stefan’s law, hold

constant and evaluate

. For Wien’s displacement law, set

.

http://z8.invisionfree.com/DYK/index.php?showtopic=867

Last edited by JaneFairfax (2009-09-24 03:51:09)

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Science laws and theorems

Three functions

Note:All three of the above mentioned functions are multiplicative,which means that:

Euler's formula

Note:

is not always the smallest number for which the above identity can hold.

Last edited by anonimnystefy (2012-03-16 01:07:37)

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“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Science laws and theorems

Lowest Common Multiple Identity

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“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.