#A TESSELLATION FREE#

The pattern that is formed is called a tessellation. (you may refer to the examples on pages 102 and 103 of EGT.Tessellation If many copies of a shape can be used to cover a surface, without leaving any gaps between them, then we say that the shape will tessellate. Give an example satisfying one but not the other. For any two definitions above which are not equivalent,.Which of the above definitions of 'tessellation'Īre equivalent (i.e.In each of the above definitions of 'tessellation'.Regular tessellations are made up entirely of congruent regular polygons Resulting from the arrangement of regular polygons to coverĪ plane without any interstices (gaps) or overlapping. In geometrical terminology a tessellation is a pattern.Identically arranged at every vertex point.Ī tessellation is a regular tiling of polygons (in two dimensions),

Remember 'regular' means the sides of the polygon are all the same length,Īnd 'congruent' means that the polygons fitted together are all the same sizeĪ semi-regular (or non-periodic) tessellation is formed by a regular arrangement of polygons, Polygon covering a plane in a repeating pattern without any openings or overlaps. Is done with one repeated congruent regular

The tiling for a regular (or periodic) tessellation (usually polygons) that can be extended infinitely.

Harder - A tessellation is a repeating pattern composed of interlocking shapes.

Easier - A tessellation is created when a shape is repeated over and over again.Īll the figures fit onto a flat surface exactly together without any gaps or.

Plane figures that fills the plane with no overlaps and no gaps. A tessellation whose tiles are all congruent regular polygonsĪ tessellation or tiling of the plane is a collection of (called tiles) whose union is the entire plane and whose interiorsĪ tessellation is said to be well aligned ifĪny two regions meet either in a common edge or a common vertex

A tessellation of the plane is a collection.

(EGT page 102) with an addition we invented in class. Some I don't like because they do not have the correctįorm as explained above. Undefined notion, namely the notion of 'set'.īelow are some definitions for 'Tessellation' that I found

That all mathematics could be based on a single It was only in 1928 that mathematicians realized (and a few others) are usually left undefined in this sense. In geometry books, the terms 'point' and 'line' These terms are defined axiomatically, by specifying the laws In mathematics this means that some terms must be left undefined.

A definition is unintelligble to a reader whoĭoes not know what the genus in the definition is.

The reason is that, in mathematics, the genus is never a time. We cannot define a point except as 'something with no parts', nor blindness except as 'the absence of sight in a creature that is normally sighted'. We should not define 'wisdom' as the absence of folly, or a healthy thing as whatever is not sick.

#A TESSELLATION FREE#

(See the definition of Free will in Wikipedia, for instance).Ī definition should not be negative where it can be positive. Terms are difficult to define without obscurity. However, sometimes scientific and philosophical

The violation of this rule is known by the Latin Obscure or difficult, by the use of terms that are commonly understood and The purpose of a definition is to explain the meaning of a term which may be not include any things to which the defined term would not truly apply). not miss anything out), and to no other objects (i.e. It must be applicable to everything to which the defined term applies (i.e.

The definition must not be too wide or too narrow.

Using the term 'consequent', nor conversely. Clearly, we cannot define 'antecedent' without Note, however, that it is acceptable to define two relative terms in This error is known as circulus in definiendo. To define a horse as 'a member of the species equus' wouldįor this reason, Locke adds that a definition of a term must notĬonsist of terms which are synonymous with it. Thus 'triangle' is defined as 'a plane figure' (genus)īounded by three straight sides (differentia).Ĭertain rules have traditionally been given for thisĪ definition must set out the essential attributes of the thing defined. (the distinguishing feature which marks it off from other Of things to which the defined thing belongs, Here is an explanation of how definitions Definition and Tessellation Definition and Tessellation