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Page 1: © T Madas. A pattern of shapes which fit together without leaving any gaps or overlapping A way of completely covering a plane with shapes which do not

© T Madas

http://images.google.co.uk/imgres?imgurl=www.shodor.org/interactivate/discussions/images/nosymmetry.gif&imgrefurl=http://www.shodor.org/interactivate/discussions/tesssymmetry.html&h=238&w=412&prev=/images%3Fq%3Dtessellations%26svnum%3D10%26hl%3Den%26lr%3D%26ie%3DUTF-8%26oe%3DUTF-8

Page 2: © T Madas. A pattern of shapes which fit together without leaving any gaps or overlapping A way of completely covering a plane with shapes which do not

© T Madas

A pattern of shapes which fit together without leaving any gaps or overlapping

A way of completely covering a plane with shapes which do not overlap.

W h a t i s a t e s s e l l a t i

o n?

Page 3: © T Madas. A pattern of shapes which fit together without leaving any gaps or overlapping A way of completely covering a plane with shapes which do not

© T Madas

A regular tessellation uses identical regular polygons to fill the plane.

There are only 3 regular tessellations, using squares, equilateral triangles or regular hexagons.

What is a Regular Tessellation ?

Page 4: © T Madas. A pattern of shapes which fit together without leaving any gaps or overlapping A way of completely covering a plane with shapes which do not

© T Madas

Archimedean Tessellationsor semi-regular tessellations

These are tessellations using only regular polygons, with two or more different polygons around each vertex with each vertex having the same pattern of polygons round it.

Page 5: © T Madas. A pattern of shapes which fit together without leaving any gaps or overlapping A way of completely covering a plane with shapes which do not

© T Madas

There are 8 Archimedean Tessellations:

triangles and squares

triangles and hexagons

triangles and dodecagons

squares, hexagons and dodecagons

squares and octagons

triangles, squares and hexagons

Page 6: © T Madas. A pattern of shapes which fit together without leaving any gaps or overlapping A way of completely covering a plane with shapes which do not

© T Madas

triangles, squares and hexagons

Page 7: © T Madas. A pattern of shapes which fit together without leaving any gaps or overlapping A way of completely covering a plane with shapes which do not

© T Madas

triangles, squares and hexagons

Page 8: © T Madas. A pattern of shapes which fit together without leaving any gaps or overlapping A way of completely covering a plane with shapes which do not

© T Madas

Page 9: © T Madas. A pattern of shapes which fit together without leaving any gaps or overlapping A way of completely covering a plane with shapes which do not

© T Madas

This tessellation is not regular or semi-regular.Can you explain why?

Page 10: © T Madas. A pattern of shapes which fit together without leaving any gaps or overlapping A way of completely covering a plane with shapes which do not

© T Madas

Page 11: © T Madas. A pattern of shapes which fit together without leaving any gaps or overlapping A way of completely covering a plane with shapes which do not

© T Madas

Page 12: © T Madas. A pattern of shapes which fit together without leaving any gaps or overlapping A way of completely covering a plane with shapes which do not

© T Madas

Tessellations can be made using all sorts of shapes

Page 13: © T Madas. A pattern of shapes which fit together without leaving any gaps or overlapping A way of completely covering a plane with shapes which do not

© T Madas

Tessellations can be made using all sorts of shapes

Page 14: © T Madas. A pattern of shapes which fit together without leaving any gaps or overlapping A way of completely covering a plane with shapes which do not

© T Madas

This is where Mathematics meets Art

Page 15: © T Madas. A pattern of shapes which fit together without leaving any gaps or overlapping A way of completely covering a plane with shapes which do not

© T Madas

Maurits Cornelius Escher1898-1972

The most famous mathematical artist is the Dutchman, Escher

Page 16: © T Madas. A pattern of shapes which fit together without leaving any gaps or overlapping A way of completely covering a plane with shapes which do not

© T Madas

Page 17: © T Madas. A pattern of shapes which fit together without leaving any gaps or overlapping A way of completely covering a plane with shapes which do not

© T Madas

Page 18: © T Madas. A pattern of shapes which fit together without leaving any gaps or overlapping A way of completely covering a plane with shapes which do not

© T Madas

Page 19: © T Madas. A pattern of shapes which fit together without leaving any gaps or overlapping A way of completely covering a plane with shapes which do not

© T Madas

Page 20: © T Madas. A pattern of shapes which fit together without leaving any gaps or overlapping A way of completely covering a plane with shapes which do not

© T Madas

Page 21: © T Madas. A pattern of shapes which fit together without leaving any gaps or overlapping A way of completely covering a plane with shapes which do not

© T Madas

Page 22: © T Madas. A pattern of shapes which fit together without leaving any gaps or overlapping A way of completely covering a plane with shapes which do not

© T Madas

Page 23: © T Madas. A pattern of shapes which fit together without leaving any gaps or overlapping A way of completely covering a plane with shapes which do not

© T Madas

Page 24: © T Madas. A pattern of shapes which fit together without leaving any gaps or overlapping A way of completely covering a plane with shapes which do not

© T Madas

Page 25: © T Madas. A pattern of shapes which fit together without leaving any gaps or overlapping A way of completely covering a plane with shapes which do not

© T Madas

Page 26: © T Madas. A pattern of shapes which fit together without leaving any gaps or overlapping A way of completely covering a plane with shapes which do not

© T Madas

Page 27: © T Madas. A pattern of shapes which fit together without leaving any gaps or overlapping A way of completely covering a plane with shapes which do not

© T Madas

Page 28: © T Madas. A pattern of shapes which fit together without leaving any gaps or overlapping A way of completely covering a plane with shapes which do not

© T Madas

Page 29: © T Madas. A pattern of shapes which fit together without leaving any gaps or overlapping A way of completely covering a plane with shapes which do not

© T Madas

Page 30: © T Madas. A pattern of shapes which fit together without leaving any gaps or overlapping A way of completely covering a plane with shapes which do not

© T Madas

Page 31: © T Madas. A pattern of shapes which fit together without leaving any gaps or overlapping A way of completely covering a plane with shapes which do not

© T Madas

Page 32: © T Madas. A pattern of shapes which fit together without leaving any gaps or overlapping A way of completely covering a plane with shapes which do not

© T Madas

Page 33: © T Madas. A pattern of shapes which fit together without leaving any gaps or overlapping A way of completely covering a plane with shapes which do not

© T Madas

Page 34: © T Madas. A pattern of shapes which fit together without leaving any gaps or overlapping A way of completely covering a plane with shapes which do not

© T Madas

Page 35: © T Madas. A pattern of shapes which fit together without leaving any gaps or overlapping A way of completely covering a plane with shapes which do not

© T Madas

Page 36: © T Madas. A pattern of shapes which fit together without leaving any gaps or overlapping A way of completely covering a plane with shapes which do not

© T Madas

Page 37: © T Madas. A pattern of shapes which fit together without leaving any gaps or overlapping A way of completely covering a plane with shapes which do not

© T Madas

Page 38: © T Madas. A pattern of shapes which fit together without leaving any gaps or overlapping A way of completely covering a plane with shapes which do not

© T Madas

another tessellating pattern

Page 39: © T Madas. A pattern of shapes which fit together without leaving any gaps or overlapping A way of completely covering a plane with shapes which do not

© T Madas

Page 40: © T Madas. A pattern of shapes which fit together without leaving any gaps or overlapping A way of completely covering a plane with shapes which do not

© T Madas

Page 41: © T Madas. A pattern of shapes which fit together without leaving any gaps or overlapping A way of completely covering a plane with shapes which do not

© T Madas

Page 42: © T Madas. A pattern of shapes which fit together without leaving any gaps or overlapping A way of completely covering a plane with shapes which do not

© T Madas

Page 43: © T Madas. A pattern of shapes which fit together without leaving any gaps or overlapping A way of completely covering a plane with shapes which do not

© T Madas

Page 44: © T Madas. A pattern of shapes which fit together without leaving any gaps or overlapping A way of completely covering a plane with shapes which do not

© T Madas

Page 45: © T Madas. A pattern of shapes which fit together without leaving any gaps or overlapping A way of completely covering a plane with shapes which do not

© T Madas

LOAD BEARING SHAPES€¦ · LOAD BEARING SHAPES Which shape is the strongest? Circle, Triangle, or Square In this activity, students will learn which shaped column will hold the most

Which shapes and polygons can you find in this picture?

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Shapes Preschool. Circles and Ovals Let’s trace the shapes and see which object they match!

© T Madas Trial and Improvement Practice. © T Madas Find 2 consecutive prime numbers less than 50 which add up to 90 43 + 47 = 90 Find 2 consecutive odd

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© T Madas 276-194 B.C.. © T Madas Eratosthenes was born in Cyrene which is now in Libya in North Africa and was a friend of Archimedes. His teachers included

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© T Madas. Use 1 regular hexagon and 6 half hexagons to fill a bigger regular hexagon Filling up 2D space with shapes Use 3 regular hexagons and 7 equilateral

(1) Which shapes are divided into two mirror halves by the

tugas 1 madas uas

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Stellating shapes - AMSP · 2020-07-09 · Stellating shapes Stellating shapes can create exciting and different polygons. We can investigate which shapes can be stellated, how they

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C 5 Geometry of 2D shapes · CHAPTER 5: GEOMETRY OF 2D SHAPES 115 5 Geometry of 2D shapes 5.1 Triangles, quadrilaterals, circles and others DECIDE WHICH IS WHICH AND DRAW SOME FIGURES

© T Madas Calculating Percentages using a Calculator

© T Madas Time Height © T Madas Time Height Liquid is poured in the container at constant rate

combinations and permutations - MadAsMaths · 2017. 3. 22. · Created by T. Madas Created by T. Madas Question 13 (****) Alex, Beth and Cain are 3 students in a class which consists

© T Madas. 2 shapes which are identical are called: Congruent Which transformations produce congruent images? Congruent shapes have: Equal lengths angles

indices exam questions - MadAsMathsmadasmaths.com/.../basic_topics/various/indices_exam_questions.pdf · Created by T. Madas Created by T. Madas Question 2 (**) a) Evaluate the following

Metal-Amplified Density Assays, (MADAs), including a

La constitucionalización de las fuerzas ar madas

goodness of fit - MadAsMaths · GOODNESS OF FIT . Created by T. Madas Created by T. Madas DISCRETE DATA . Created by T. Madas Created by T. Madas Question 1 The number of car immobilizations,

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© T Madas Composite Shapes with Circular Parts

Which Shapes and Forms Are the Strongest?

differentiation practice ii exam questions - MadAsMathsmadasmaths.com/archive/maths_booklets/standard_topics/... · 2020. 7. 21. · Created by T. Madas Created by T. Madas Question

Created by T. Madas - Jazzy Maths · 2020. 1. 31. · Created by T. Madas Created by T. Madas Question 11 (***+) The figure above shows a curve known as a re-entrant cycloid, with