# Similarity

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## Similarity

a concept in geometry. Geometric figures are said to be similar if they are identical in shape, regardless of whether they are identical in size. The figures F1 and F2 are similar if between their points a one-to-one correspondence can be established such that the ratio of the distances between any two pairs of corresponding points of F1 and F2 a constant k. This constant is called the similarity factor. The angles between corresponding lines of similar figures are equal. Thus, in Figure 1 ∠B1A11C1 = ∠B2A2C2 = ϕ. The ratio of the areas of bounded similar figures is equal to the square of the similarity factor, and the ratio of the volumes of similar solids is equal to the cube of the similarity factor.

Figure 1

A geometric transformation of the plane (or of space) such that all figures in the plane are transformed into similar figures with the same ratio of similitude is called a similarity transformation, which is a special case of an affine transformation. The set of all similarity transformations of the plane or of space forms a group. Any similarity transformation can be represented as the successive application of a homothetic transformation and a proper or improper motion.

The concept of similarity and similarity transformations are used in such engineering applications of geometry as modeling and drawing. For example, the operation of the pantograph is based on the concept of similarity.

References in periodicals archive ?
Open Mic and Karaoke are similiar but Karaoke is more lipsyncing than actual singing as a talented artist.
22 (BNA) Green technology has the potential to become a key driver for growth, employment and technology in Malaysia, similiar to the situation in Germany.
I READ with some interest that the Isa Town flyover should have been given to a local company because they have large numbers of Bahrainis working for them on similiar projects.
Lessons learned should be studied by our nation's disaster experts and changes should be made to prepare the United States for such events, otherwise such disasters will be on a mass scale similiar to Bosnia, Haiti and 9/11.
Earlier in March, Iran's deputy Army chief, General Muhammad Reza Ashtiani, had made a similiar remark, where he had warned that Iran would eliminate Israel if it attacks the Islamic republic.
Capello has first-hand experience of Raul s influence after coaching him during two spell as Real manager and he believes Rooney has the ability to have a similiar inspirational effect on England.
The technology behind the optical disk is the foundation for similiar formats including CDs and DVDs.
Just 48 hours after defender Martin Laursen revealed his desire to one day captain Villa, it appears his manager is of a similiar view, writes Lisa Smith.
Rethink say there is growing evidence the health risks associated with cannabis use means warnings similiar to those on tobacco products are necessary.
The Arsenal boss (below) believes bitter rival Mourinho wanted to create a long-term legacy at Stamford Bridge, similiar to Sir Alex Ferguson's at Old Trafford and his own.
In the Youngstown Steel case during the Truman Administration, a precedent-setting case on Presidential overreaching, Justice Felix Frankfurter demolished a similiar argument: "It is one thing to draw an intention of Congress from general language and to say that Congress would have explicitly written what is inferred.
British Chicken Marketing took similar steps last year when there was a similiar media frenzy.

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