Definition:Similar Figures/Informal Definition
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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.
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
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): similar (of figures)