Polya, Analogy

Front 1

What is the preliminary definition of analogy as given by Polya? What initial example did he use to illustrate this?

Back 1

rectangular parallelogram <=> rectangular parallelepiped
Linked by a bounding element

Front 2

What is the example of the analogous problem used in section 15?

Back 2

parallelogram - diagonal - rectangle

Front 3

In the principle example in the section (for finding the centre of gravity), what is the principle stated by Polya with regards to systems of masses?

Back 3

If a system of masses has S parts, and if each of the COG of these parts lies in the same plane, then the COG of the system of masses also lies in this plane.

Front 4

Outline the proof for the COG of a triangle.

Back 4

Thin slice triangle
Three viewpoints
Coincidence of medians
Prove by geometry

Front 5

Outline the proof for the COG of a tetrahedron.

Back 5

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Front 6

How was the method of the analogous problem used to prove the COG of the tetrahedron?

Back 6

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Front 7

How was the RESULT of the analogous problem used to prove the intersection of medians of the tetrahedron?

Back 7

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Front 8

What analogies (give two) can be made between the line, the triangle and the tetrahedron?

Back 8

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Front 9

Give examples of an inference by analogy (based on the line-triangle-tetrahedron analogy)

Back 9

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Front 10

Give "real life" examples of inference by analogy

Back 10

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Front 11

Give two examples where analogy reaches the point of mathematical precision.

Back 11

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