58 results for “theorem”
Expands any power of a binomial into a sum of terms.
Relates the sides of a right triangle.
Powers of complex numbers in trig form.
Connects differentiation and integration.
Guarantees a point where the tangent equals the average slope.
Updates a probability given new evidence.
Reverses conditional probabilities using prior knowledge.
Relates rank and null space dimension to columns.
An object stays at rest or in uniform motion unless acted on by a net force.
Net force equals mass times acceleration (rate of change of momentum).
For every action there is an equal and opposite reaction.
Total momentum of an isolated system stays constant.
Energy cannot be created or destroyed, only transformed.
Buoyant force equals the weight of fluid displaced.
Pressure applied to a confined fluid transmits equally in all directions.
Faster-moving fluid has lower pressure (energy conservation in flow).
The restoring force of a spring is proportional to its extension.
Every mass attracts every other mass.
Planets orbit the Sun in ellipses with the Sun at one focus.
A line from a planet to the Sun sweeps equal areas in equal times.
The square of the orbital period is proportional to the cube of the semi-major axis.
Two systems in thermal equilibrium with a third are in equilibrium with each other.
Energy conservation: change in internal energy equals heat added minus work done.
The entropy of an isolated system never decreases.
At constant temperature, pressure and volume of a gas are inversely proportional.
At constant pressure, volume of a gas is proportional to absolute temperature.
At constant volume, pressure of a gas is proportional to absolute temperature.
Total energy radiated by a black body scales with the fourth power of temperature.
Voltage across a resistor equals current times resistance.
Electrostatic force between two point charges.
Electric flux through a closed surface is proportional to the enclosed charge.
A changing magnetic flux induces an electromotive force.
Induced current opposes the change in flux that produced it.
A magnetic field circulates around an electric current.
Current into a junction equals current out of it (charge conservation).
The sum of voltages around any closed loop is zero.
Relates focal length to object and image distances for a thin lens.
Light bends when passing between media of different refractive index.
Mass and energy are equivalent and interconvertible.
The energy of a photon is proportional to its frequency.
Position and momentum cannot both be known with unlimited precision.
An object stays at rest or in uniform motion unless acted upon.
Every action has an equal and opposite reaction.
Total momentum is conserved without external forces.
Total electric charge in an isolated system is conserved.
Change in internal energy equals heat added minus work done.
Total entropy of an isolated system never decreases.
Elastic restoring force is proportional to displacement.
A changing magnetic flux induces an EMF.
Induced currents oppose the change producing them.
Buoyant force equals the weight of displaced fluid.
Pressure applied to a confined fluid transmits undiminished.
Holds when p is prime and gcd(a,p)=1.
Approximates the number of primes below x.
A primality criterion for p.
Analyzes running time of divide-and-conquer algorithms.
General form for analyzing divide-and-conquer recurrences.