Proving Q & I: Euler's Formula Needed

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In summary, Euler's formula is a mathematical equation discovered by Swiss mathematician Leonhard Euler in the 18th century. It relates the number of faces, vertices, and edges of a convex polyhedron through the formula F + V - E = 2. This formula is important in geometry and topology as it has been proven to hold true for all convex polyhedra. It can also be used in proving Q & I (Quintuple and Inequality) and has real-life applications in fields such as architecture, computer graphics, and engineering. However, it cannot be applied to non-convex polyhedra due to their different properties.
  • #1
SoulofLoneWlf
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Well just wondering if anyone knew of a place where i could find a proof for electricity and magnetism since it seems i will be needing a lot of these for example

prove
Q = Re(Ae^(i[Phi])e^(i[omega]t))

or show that I moving through a capacitor
I = Re(i[omega]Ae^i[phi] e^{i[omega]t

i mean looking at it, it will need eulers formula but how?
 
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  • #2
google "phasors"
 
  • #3
Awesome thanks should get me started :D
 

1. What is Euler's formula?

Euler's formula is a mathematical equation discovered by Swiss mathematician Leonhard Euler in the 18th century. It states that for any convex polyhedron, the number of faces (F), vertices (V), and edges (E) are related by the formula F + V - E = 2.

2. Why is Euler's formula important?

Euler's formula is important because it relates three fundamental properties of a polyhedron - its faces, vertices, and edges. This formula has been proven to hold true for all convex polyhedra, making it a powerful tool in geometry and topology.

3. How is Euler's formula useful in proving Q & I?

Euler's formula can be used in proving Q & I (Quintuple and Inequality) by providing a key piece of evidence in the mathematical proof. By showing that Euler's formula holds true for all convex polyhedra, it supports the claim that Q & I are also true for all convex polyhedra.

4. Can Euler's formula be applied to non-convex polyhedra?

No, Euler's formula only applies to convex polyhedra. This is because convex polyhedra have certain properties that allow for the formula to hold true, such as all edges lying on a single plane. Non-convex polyhedra do not have these same properties.

5. Are there any real-life applications of Euler's formula?

Yes, Euler's formula has many real-life applications in fields such as architecture, computer graphics, and engineering. It can be used to calculate the number of vertices, edges, and faces in complex structures, and has also been applied in computer algorithms for solving geometric problems.

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