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From triangles to circles: Do you know the mysterious classification of various shapes?
Shape, as a graphical representation of an object that encompasses its outer boundaries or outline, is distinguished from other properties of the object such as color, texture, and material type. In geometry, shape does not include information about the object's position, size, orientation, and chirality. It can be said that a figure is a representation that includes shape and size, and depending on the shape, it can be classified as a flat shape or a three-dimensional shape.
Classification of simple shapes
Many simple shapes can be grouped into several broad categories. For example, polygons are classified into triangles, quadrilaterals, pentagons, etc. based on the number of sides. Each type of shape can be subdivided. Triangles can be divided into equilateral triangles, isosceles triangles, obtuse triangles, acute triangles, scalene triangles, etc., while quadrilaterals can be rectangles, rhombuses, trapezoids, squares, etc.
Other common shapes include points, lines, planes, and conic sections such as ellipses, circles, and parabolas.
Shapes in geometry
Geometric shape refers to the geometric information left after removing position, proportion, direction and reflection. In other words, when a shape is moved, enlarged, rotated, or reflected in a mirror, the resulting shape is identical to the original shape, rather than creating an entirely new shape. Many two-dimensional geometric shapes can be defined by a set of points or vertices and lines connecting the points. These shapes are called polygons, including triangles, squares, and pentagons.
Shape properties
There are several ways to compare the shapes of two objects:
- Equality: Two objects are equal if one object can be transformed into another object through a sequence of rotations, translations, and/or reflections.
- Similarity: Two objects are similar if one object can be transformed into another through uniform scaling, and subsequent rotation, translation, and/or reflection.
- Congruent: Two objects are congruent if one can be transformed into another through a series of deformations without tearing the object or punching holes in it.
Sometimes, even similar or equal objects may be perceived as having different shapes in certain contexts.
Equivalence of shapes
In geometry, if one set of points can be transformed into another set of points by a combination of translation and rotation and uniform scaling, then the two subsets have the same shape. Shape information does not depend on the object's size and placement in space. For example, the letters "d" and "p" have the same shape because they overlap perfectly by simply translating the "d" a specific distance, rotating it, and enlarging it. However, mirror images may be viewed as different shapes.
Human body’s perception of shape
Human vision relies on extensive shape representations. Some psychologists theorize that humans mentally break down images into simple geometric shapes such as cones and spheres, also known as "terrain models." In addition, shape similarity comparison requires at least 22 independent dimensions to describe natural shape variations. Can we use the analysis of shape to gain a deeper understanding of the objects we design and build?
