Similarity (geometry)
Similarity is an idea in geometry. It means that two polygons, line segments, or other figures can become the same via resizing. Similar objects do not need to have the same size. Two shapes are similar if their angles have the same measure and their sides are proportional. Two circles, squares, or line segments are always similar. If figure [math]\displaystyle{ F }[/math] is similar to figure [math]\displaystyle{ F' }[/math], then we write [math]\displaystyle{ F \sim F' }[/math].[1][2][3]
Similarity is very similar to congruence. Congruent shapes have the same sides and angles. Because of that, two shapes are congruent to each other if one can become another through rotating, reflecting or moving only.[2] In fact, all shapes that are congruent to each other are also similar, but not vice versa.
Related pages
References
- ↑ "Compendium of Mathematical Symbols". Math Vault. 2020-03-01. Retrieved 2020-09-21.
- ↑ 2.0 2.1 "Similar". www.mathsisfun.com. Retrieved 2020-09-21.
- ↑
Similarity (geometry) Media
exemple de L semblables directement ou indirectement
similitude directe: translation
Similitude directe : rotation
similitude indirecte : reflexion
similitude directe : homothétie
Similar rectangles
The tessellation of the large triangle shows that it is similar to the small triangle with an area ratio of 5. The similarity ratio is \tfrac{5}{h} = \tfrac{h}{1} = \sqrt 5. This can be used to construct a non-periodic infinite tiling.
Sierpiński triangle. A space having self-similarity dimension \tfrac{\log 3}{\log 2} = \log_2 3, which is approximately 1.58. (From Hausdorff dimension.)
A self-similar set constructed with two similitudes: *\begin{align} *z' &= 0.1[(4+i)z+4] \\*z' &= 0.1[(4+7i)z^* + 5 - 2i]*\end{align}
Weisstein, Eric W. "Similar". mathworld.wolfram.com. Retrieved 2020-09-21.
