Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

You are not logged in.

- Topics: Active | Unanswered

**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 16,367

**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.

Second law:- The rate of change of momentum is directly proportional to the applied force and takes place in the direction of the force.

Third law:- Every action has an equal and opposite reaction.

Character is who you are when no one is looking.

Offline

**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 16,367

** Law of gravitation.**

The law that every two particles of matter in the universe attract each other with a force that acts along the line joining them, and has a magnitude proportional to the product of their masses and inversely proportional to the square of the distance between them.

Character is who you are when no one is looking.

Offline

**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 16,367

**Kepler's laws of planetary motion:-**

First law

The first law of Kepler states that a planet moves in an elliptical orbit around the Sun that is located at one of the two foci of the ellipse.

Second law

The second law states that the radius vector of the ellipse (the imaginary line between the planet and the Sun) sweeps out areas that are proportional to time.

Third law

Kepler's third law defines the relations that hold within the system of planets. It states that the ratio between the square of a planet's period (the time required to complete one orbit) to the cube of the mean radius (the average distance from the Sun during one orbit) is a constant.

Character is who you are when no one is looking.

Offline

**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 16,367

**Law of reflection**

law of reflection

As applied to rays of light, sound, or radiant heat which strike a surface: the angle of reflection is equal to the angle of incidence, and the reflected and incident rays are in the same plane with a perpendicular to the surface.

Character is who you are when no one is looking.

Offline

**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 16,367

**Law of refraction**

In optics and physics, Snell's law (also known as Descartes' law or the law of refraction), is a formula used to describe the relationship between the angles of incidence and refraction, when referring to light or other waves, passing through a boundary between two different isotropic media, such as air and glass. The law says that the ratio of the sines of the angles of incidence and of refraction is a constant that depends on the media.

In optics, the law is used in ray tracing to compute the angles of incidence or refraction, and in experimental optics to find the refractive index of a material.

Character is who you are when no one is looking.

Offline

**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 16,367

**Pascal's law**

The law that a confined fluid transmits externally applied pressure uniformly in all directions, without change in magnitude.

Character is who you are when no one is looking.

Offline

**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 16,367

**Laws of Thermodynamics**

Zeroth law

If two thermodynamic systems are each in thermal equilibrium with a third, then they are in thermal equilibrium with each other."

First law

In any process, the total energy of the universe remains constant."

Second law

The entropy of an isolated system not in equilibrium will tend to increase over time, approaching a maximum value at equilibrium. "

Third law

As temperature approaches absolute zero, the entropy of a system approaches a constant."

Character is who you are when no one is looking.

Offline

**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 16,367

**Archimedes' Principle**

Archimedes' principle, principle that states that a body immersed in a fluid is buoyed up by a force equal to the weight of the displaced fluid. The principle applies to both floating and submerged bodies and to all fluids, i.e., liquids and gases.

Character is who you are when no one is looking.

Offline

**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 16,367

**Law of conservation of energy**

Energy in a system may take on various forms (e.g. kinetic, potential, heat, light). The law of conservation of energy states that energy may neither be created nor destroyed. Therefore the sum of all the energies in the system is a constant.

Character is who you are when no one is looking.

Offline

**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 16,367

**Law of conservation of momentum**

The law of conservation of momentum is a fundamental law of nature, and it states that the total momentum of a closed system of objects (which has no interactions with external agents) is constant.

Character is who you are when no one is looking.

Offline

**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 16,367

**Ohm's law**

Ohm's law states that, in an electrical circuit, the current passing through a conductor between two points is directly proportional to the potential difference (i.e. voltage drop or voltage) across the two points, and inversely proportional to the resistance between them.

The mathematical equation that describes this relationship is:

where I is the current in amperes, V is the potential difference between two points of interest in volts, and R is a constant, measured in ohms (which is equivalent to volts per ampere), and is called the resistance. The potential difference is also known as the voltage drop, and is sometimes denoted by E or U instead of V.

Character is who you are when no one is looking.

Offline

**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 16,367

**Faraday's laws of Electrolysis:**

Faraday's 1st Law of Electrolysis

The mass of a substance produced at an electrode during electrolysis is directly proportional to the number of electrons (the quantity of electricity) transferred at that electrode.

Faraday's 2nd Law of Electrolysis

The number of faradays of electric charge required to discharge one mole of substance at an electrode is equal to the number of "excess" elementary charges on that ion.

Modern form

In modern form, Faraday's laws are summarised by:

where

m is the mass of the substance produced at the electrode,

Q is the total electric charge passed through the solution,

n is the valence number of ions of the substance (electrons transferred per ion),

F = 96 485 C mol-1 is the Faraday constant,

M is the molar mass of the substance.

T is the total amount of time of the electrolysis.

In the simple case of constant current electrolysis this reduces to:

Q = It

Character is who you are when no one is looking.

Offline

**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 16,367

**Heisenberg Uncertainity Principle**

In quantum physics, the Heisenberg uncertainty principle is the statement that locating a particle in a small region makes the momentum of the particle uncertain, and conversely, measuring the momentum of a particle precisely makes the position uncertain.

In quantum mechanics, the position and momentum do not have precise values, but have a probability distribution. There are no states in which a particle has both a definite position and momentum. The narrower the probability distribution is in position, the wider it is in momentum.

Character is who you are when no one is looking.

Offline

**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 16,367

**Pauli exclusion principle**

"No two electrons or protons or neutrons in a given system can be in states characterized by the same set of quantum numbers."

Assertion proposed by Wolfgang Pauli that no two electrons in an atom can be in the same state or configuration at the same time. It accounts for the observed patterns of light emission from atoms. The principle has since been generalized to include the whole class of particles called fermions. The spin of such particles is always an odd whole-number multiple of 1/2. For example, electrons have spin 1/2, and can occupy two distinct states with opposite spin directions. The Pauli exclusion principle indicates, therefore, that only two electrons are allowed in each atomic energy state, leading to the successive buildup of orbitals around the nucleus. This prevents matter from collapsing to an extremely dense state.

Character is who you are when no one is looking.

Offline

**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 16,367

**Coulomb's law**

The magnitude of the electrostatic force between two point electric charges is directly proportional to the product of the magnitudes of each charge and inversely proportional to the square of the distance between the charges.

Character is who you are when no one is looking.

Offline

**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 16,367

**Boyle's law**

For a fixed amount of gas kept at a fixed temperature, P and V are inversely proportional (while one increases, the other decreases).

{P= Pressure, V=Volume}

**Charle's law**

At constant pressure, the volume of a given mass of an ideal gas increases or decreases by the same factor as its temperature (in kelvin) increases or decreases.

**Ideal Gas law**

The ideal gas law is the equation of state of a hypothetical ideal gas, first stated by Benoît Paul Émile Clapeyron in 1834.

The state of an amount of gas is determined by its pressure, volume, and temperature according to the equation:

PV=nRT

where

P is the absolute pressure,

V is the volume of the vessel,

n is the amount of substance of gas,

R is the ideal gas constant,

T is the absolute temperature.

The appropriate value of the ideal gas constant (R) depends on the units being used. In SI units, R = 8.314 J mol-1 K-1 (or equivalently m³ Pa K-1 mol-1).

Character is who you are when no one is looking.

Offline

**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 16,367

** Avogadro's hypothesis**

Avogadro's law (Avogadro's Hypothesis, or Avogadro's Principle) is a gas law named after Amedeo Avogadro, who in 1811 hypothesized that:

Equal volumes of ideal or perfect gases, at the same temperature and pressure, contain the same number of particles, or molecules.

Character is who you are when no one is looking.

Offline

**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 16,367

** Fermat's Little theorem**

Fermat's little theorem states that if p is a prime number, then for any integer a, (a^p − a) will be evenly divisible by p. This can be expressed in the notation of modular arithmetic as follows:

A variant of this theorem is stated in the following form: if p is a prime and a is an integer coprime to p, then (a^(p − 1) − 1) will be evenly divisible by p. In the notation of modular arithmetic:

Another way to state this is that if p is a prime number and a is any integer that does not have p as a factor, then a raised to the p-1 power will leave a remainder of 1 when divided by p.

Fermat's little theorem is the basis for the Fermat primality test.

Character is who you are when no one is looking.

Offline

**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 16,367

**Pythagorean Theorem**

The theorem that the sum of the squares of the lengths of the sides of a right triangle is equal to the square of the length of the hypotenuse.

Character is who you are when no one is looking.

Offline

**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 16,367

**Goldbach's conjecture:-**

The unestablished conjecture that every even number except the number 2 is the sum of two primes.

Character is who you are when no one is looking.

Offline

**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 16,367

**Fermat's Last Theorem**

The theorem that the equation

has no solutions in positive integers a, b, c if n is an integer greater than 2. It was stated as a marginal note by Pierre de Fermat around 1630 and not proved until 1994 by the British mathematician Andrew Wiles (born 1953).

Character is who you are when no one is looking.

Offline

**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 16,367

** Bernoulli's theorem **

An expression of the conservation of energy in the steady flow of an incompressible, inviscid fluid; it states that the quantity (p/ρ) + gz + (v²/2) is constant along any streamline, where p is the fluid pressure, v is the fluid velocity, ρ is the mass density of the fluid, g is the acceleration due to gravity, and z is the vertical height. Also known as Bernoulli equation; Bernoulli law.

Character is who you are when no one is looking.

Offline

**Daniel123****Member**- Registered: 2007-05-23
- Posts: 663

**Wien's Law**

For a star, there is a connection between the maximum wavelength of the radiation it emits, and its temperature.

Where lambda represents the wavelength, C a constant with the value 2.898 x 10[sup]-3[/sup] mK, and T is the temperature in Kelvin.

**Stefan Boltzmann's Law**

This law decribes how the luminosity of a star depends on its temperature and surface area. (assuming the star is roughly spherical)

Where L is the luminosty in Watts, r is the radius of the star in metres, T is the temperature in Kelvin, and sigma is Stefan's constant - with the value of 5.67 x 10[sup]-8[/sup] W m[sup]-2[/sup]K[sup]-4[/sup]

**Intensity**

The intensity (power per square metre) emmited by a star can be calculated using the following formula:

Where I is the intensity measured in Watts per metre squared, L is the luminosity, and D is the distance between the star and the Earth (or the radius of the sphere of radiation emitted)

*Last edited by Daniel123 (2008-03-13 11:28:29)*

Offline

**JaneFairfax****Member**- Registered: 2007-02-23
- Posts: 6,868

**Lagranges theorem** (group theory)

The order of any subgroup *H* of a finite group *G* divides the order of *G*. The integer |*G*|⁄|*H*| is called the index of the subgroup *H* in the group *G* and is usually denoted |*G*:*H*|. Indeed, the index of *H* in *G* is precisely the number of left or right cosets of *H* in *G*.

Offline

**Daniel123****Member**- Registered: 2007-05-23
- Posts: 663

**Maxwell-Boltzmann distribution for particle velocities in an ideal gas**

Where: m = mass of a particle

k = Boltzmann constant (1.38 x 10[sup] -23 [/sup]JK-¹)

T = temperature

c = velocity of particle, defined as

When plotted on excel this produces a nice probability distribution

It's nice to see a model that uses pi and e

*Last edited by Daniel123 (2008-03-13 13:27:54)*

Offline