CK12 - Geometry

Notethat the samebasic“unit”can be usedto makedifferenttessellations.

FurtherReading

M. C. Escherwas a famoustwentieth-centurygraphicartistwho specializedin extremelyoriginal,provocative
tessellations.You can readabouthim and see manyexamplesof his art inM.C.Escher:His Life and
CompleteGraphicWork. New York: H.N. Abrams

LessonSummary

Tessellationsare at the intersectionof geometryand design.Many—butnot all—ofthe mostcommon
polygonswill tessellate;somewill not. Someof the regularpolygonswill tessellateby themselves.Semi-
regulartessellationsare madeup of two (or more)of the regularpolygons.Thereis no needto limit tessel-
lationsto regularpolygonsor even to polygons.Anyonecan draw a tessellation,usingwhatevershapedesired
as long as it will, in fact, tessellate.

The repetitivepatternsthat maketessellationsare relatedto transformations.For example,a tessellation
may consistof a basicunit that is repeatedlytranslatedor reflected.

Pointsto Consider

All tessellationsshowsomekind of symmetry. Why?Becausethat is a naturalresultof creatinga pattern
throughreflectionor translation.We will examinesymmetrymorethoroughlyin an upcominglesson.

Tessellationscan also be createdthroughrotations.Just as we haveseencompositetransformations,there
are also compositetessellationsthat use two or moretransformations.

Lookaroundin your daily life. Wheredo you see tessellations?

LessonExercises

Will the givenshapetessellate?If the answeris yes, makea drawingon grid paperto showthe tessellation.
(D1)

1. A square


2. A rectangle


3. A rhombus


4. A parallelogram


5. A trapezoid


6. A kite


7. A completelyirregularquadrilateral


8. Whichregularpolygonswill tessellate?


9. Use equilateraltrianglesand regularhexagonsto drawa semiregulartessellation.

Answers

1. Yes


2. Yes