Law, Principles and Theorems

• Bernoulli's Energy Theorem


  The sum of pressure, the potential energy per unit volume, and the kinetic energy per unit volume has the same value at any two points along a streamline in an ideal fluid in steady state flow
• Coulumb's Law


  The force between two charges directly varies as the magnitude of each charge and inversely as the square of the distance between them
• Goldbach Conjecture


  Every integer greater than two can be written as the sum of two prime
• Fundamental Theorem of Arithmetic


  Every positive integer greater than 1 is a prime or can be expressed as a unique product of primes and powers
• Vinogradov's Theorem


  Every sufficiently large off numbers can be expressed as a sum of these prime numbers
• Fermat's Theorem


  If n>2 the equation x + y = 2n cannot be solved in positive integers x, y, and z
• Pascal's Law


  If an external pressure is applied in a confined fluid, the pressure will be increased at every point in the fluid by the amount of external pressure
• Fibonacci Theorem


  A sequence of numbers where the numbers are equal to the sum of the two preceding numbers such as 1, 1, 2, 3, 5, 8, 13, 21 ...
• Dirichlet Theorem


  Theorem in every arithmetic progression a, a+d, a+2d, ...
• Cramer's Rule


  Method of solving linear equation with several unknowns simultaneously using determinants
• Number Theory


  Study of the properties of positive integers
• Pythagorean Theorem


  Most proved theorem in mathematics
• Fermat's Theorem


  Least proved theorem in mathematics
• Moilweide's Equation


  Equation used for checking the solution of plane triangle
• Napier's Rule


  The sine of any middle part is equal to the product of the cosine of the opposite parts
• Napier's Rule


  The sine of any middle part is equal to the product of the tangent of the adjacent part
• Chain Rule


  Also known as the composite function rule
• First Proposition of Pappus

  The area of the surface generated by rotating any place R curve about a certain axis in its plane is equal to the product of the length of the arc and the distance travelled by its centroid
• Second Proposition of Pappus

  The volume of any solid is equal to the generating area times the circumference of the circle described by the centroid of the area
• Varignon's Theorem


  The moment of the resultant of two concurrent forces with respect to a center of their planes is equal to the algebraic sum of the moments of the components with respect to the same center
• Archimedes Principle


  A body immersed in a fluid is subjected to a buoyant force which is equal to the weight of the fluid displaced
• Kepler's Law


  Law which describes the motion of stars, planets and comets
• Newton's First Law of Motion


  A body in its state of rest or at constant speed in a straight line motion is compelled to change that state because of forces acting on it
• Newton's Second Law of Motion

  An unbalanced force acting on an object will cause the object to accelerate in the direction of the force. Similar to d'Alembert's Principle F=ma
• Newton's Third Law of Motion

  For every action there is always an equal and opposite reaction
• Kepler's First Law (Law of Ellipses)


  The path of the planets about the sun is elliptical in shape, with the center of the sun being located at one focus
• Kepler's Second Law (Law of Equal Areas)


  An imaginary line drawn from the center of the sun to the center of the planet will sweep out equal areas in equal intervals of time
• Kepler's Third Law (Law of Harmonies)


  The ratio of the squares of the periods of any two planets is equal to the ratio of the cubes of their average distances from the sun