Definition:Similar Figures
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Definition
Two rectilineal figures are similar if and only if:
- They have corresponding angles, all of which are equal
- They have corresponding sides, all of which are proportional.
Informal Definition
Two geometric figures are similar if they have the same shape but not necessarily the same size.
It is intuitively understood what it means for two figures to have the same shape.
Algebraic Definition
Two geometric figures are similar if one can be transformed into the other by means of a similarity mapping.
Euclid's Definition
In the words of Euclid:
- Similar rectilineal figures are such as have their angles severally equal and the sides about the equal angles proportional.
(The Elements: Book $\text{VI}$: Definition $1$)
Also see
- Results about similar figures can be found here.
Historical Note
The symbol introduced by Gottfried Wilhelm von Leibniz to denote geometric similarity was the tilde: $\sim$
This is still in use and can still be seen, but is not universal.
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): similar
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): similar
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): similar (of figures)