Hola brainlians!, Please help me from this question given below ~
Explain all the following in detail -
1) Pythagoras theorem
2) Bertrand's theorem.
3) Betti's theorem.
4) Birkhoff's theorem (electromagnetism)
5) Blondel's theorem.
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Answer:
Pythagoras Theorem:- A theorem attributed to Pythagoras that the square on the hypotenuse of a right-angled triangle is equal in area to the sum of the squares on the other two sides.
Bertrand's Theorem:- In classical mechanics, Bertrand's theorem states that among central-force potentials with bound orbits, there are only two types of central-force (radial) scalar potentials with the property that all bound orbits are also closed orbits.
Betti's Theorem:- Betti's theorem, also known as Maxwell–Betti reciprocal work theorem, discovered by Enrico Betti in 1872, states that for a linear elastic structure subject to two sets of forces {Pi} i=1,...,n and {Qj}, j=1,2,...,n, the work done by the set P through the displacements produced by the set Q is equal to the work done by the set Q through the displacements produced by the set P. This theorem has applications in structural engineering where it is used to define influence lines and derive the boundary element method.
Birkhoff's Theorem:- In general relativity, Birkhoff's theorem states that any spherically symmetric solution of the vacuum field equations must be static and asymptotically flat. This means that the exterior solution (i.e. the spacetime outside of a spherical, non-rotating, gravitating body) must be given by the Schwarzschild metric.
Blondel's Theorem:- Blondel's Theorem states that if a network is supplied through N conductors, the total power is measured by summing the readings of N wattmeters so arranged that a current element of a wattmeter is in each line and the corresponding voltage element is connected between that line and a common point.