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Aside

Unit 48 – Geometric Analogies

Difficulty: Medium/hard

Time: 3 minutes

The passage below has been adapted from How To Solve It by George Polya.

 

Analogy is a sort of similarity. Similar objects agree with each other in some respect, analogous objects agree in certain relations of their respective parts.
A rectangular parallelogram is analogous to a rectangular parallelepiped. In fact, the relations between the sides of the parallelogram are similar to those between the faces of the parallelepiped:
Each side of the parallelogram is parallel to just one other side, and is perpendicular to the remaining sides. Each face of the parallelepiped is parallel to just one other face, and is perpendicular to the remaining faces. Let us agree to call a side a “bounding element” of the parallelogram and a face a “bounding element” of the parallelepiped. Then, we may contract the two foregoing statements into one that applies equally to both figures:
Each bounding element is parallel to just one other bounding element and is perpendicular to the remaining bounding elements.
Thus, we have expressed certain relations which are common to the two systems of objects we compared, sides of the rectangle and faces of the rectangular parallelepiped. The analogy of these systems consists in this community of relations.

 

1. Which of the following pairs could be said to be analogous to one another?

  • A      Kettle          Hot Water
  • B      Cigar           Cigarette
  • C      Food           Sandwich
  • D      Hat              Head

 

 

2. Analogy is to similarity as paralleliped is to:

  • A      Rectangle
  • B      Shape
  • C      Bounding element
  • D      Geometry

 

  • Answers:
    Q1: B
    A hat goes on a head. A sandwich is a type of food, and a kettle makes water hot. Physically these objects share no relation to one another. They do not ‘agree in certain relations of their physical parts’. Both cigars and cigarettes are cylindrical. They therefore agree in this relation with each other.

    Q2: B
    Analogy is a sort of similarity
    Paralleliped is a sort of shape.

    Gamsat Sample Questions

    July 1, 2012

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