![]() Within mathematics, transformations are often used to move an object from a place where it is hard to work with it to a place where it is simpler. The use of shears in the context of an algebraic problem is explored in It’s a matter of perspective. ![]() These transformations preserve the base and the height, and the distance each coin is moved is a function of its height. For instance, you may have seen an animation in which a rectangle is ‘pushed over’ to make a parallelogram or a pile of coins or playing cards pushed over to make a leaning tower. There are other types of geometric transformations. You can explore this further with Olympic rings or Teddy bear. Transformations can also help deepen our understanding of the connections between algebra and geometry Discriminating offers a good example of this way of thinking.Īll circles can be regarded as enlargements and translations of a unit circle in the standard circle formula \((x-a)^2+(y-b)^2=r^2\) the values of \(a\) and \(b\) give information about the translation and the value of \(r\) gives the enlargement scale factor. Some of these familiar transformations are explored in Which parabola?. Enlargements preserve shape and proportion, but not usually size, while stretches keep straight lines straight, but change shape and angles. We are familiar with reflecting (which preserves the mirror line), rotating (which preserves the centre-point) and translating in 2-D and 3-D geometry these all preserve both shape and size. ![]() The word transformation is used to describe functions or operations that preserve some structure, so that some characteristics of the input set are preserved in the output set, and some other characteristics are changed in a structured way. Transforming things allows us to see them from many points of view.
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