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Resources tagged with Symmetry similar to An Introduction to Galois Theory:

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Broad Topics > Transformations and their Properties > Symmetry

Dancing with Maths

Stage: 2, 3 and 4

An article for students and teachers on symmetry and square dancing. What do the symmetries of the square have to do with a dos-e-dos or a swing? Find out more?

Shuffles

Stage: 5 Challenge Level:

An environment for exploring the properties of small groups.

Paint Rollers for Frieze Patterns.

Stage: 3 and 4

Proofs that there are only seven frieze patterns involve complicated group theory. The symmetries of a cylinder provide an easier approach.

Rose

Stage: 5 Challenge Level:

What groups of transformations map a regular pentagon to itself?

Two Triangles in a Square

Stage: 4 Challenge Level:

Given that ABCD is a square, M is the mid point of AD and CP is perpendicular to MB with P on MB, prove DP = DC.

A Roll of Patterned Paper

Stage: 4 Challenge Level:

A design is repeated endlessly along a line - rather like a stream of paper coming off a roll. Make a strip that matches itself after rotation, or after reflection

A Problem of Time

Stage: 4 Challenge Level:

Consider a watch face which has identical hands and identical marks for the hours. It is opposite to a mirror. When is the time as read direct and in the mirror exactly the same between 6 and 7?

Frieze Patterns in Cast Iron

Stage: 3 and 4

A gallery of beautiful photos of cast ironwork friezes in Australia with a mathematical discussion of the classification of frieze patterns.

Symmetric Trace

Stage: 4 Challenge Level:

Points off a rolling wheel make traces. What makes those traces have symmetry?

Trominoes

Stage: 3 and 4 Challenge Level:

Can all but one square of an 8 by 8 Chessboard be covered by Trominoes?

One Reflection Implies Another

Stage: 4 Challenge Level:

When a strip has vertical symmetry there always seems to be a second place where a mirror line could go. Perhaps you can find a design that has only one mirror line across it. Or, if you thought that. . . .

Attractive Tablecloths

Stage: 4 Challenge Level:

Charlie likes tablecloths that use as many colours as possible, but insists that his tablecloths have some symmetry. Can you work out how many colours he needs for different tablecloth designs?

The Frieze Tree

Stage: 3 and 4

Patterns that repeat in a line are strangely interesting. How many types are there and how do you tell one type from another?

Rotations Are Not Single Round Here

Stage: 4 Challenge Level:

I noticed this about streamers that have rotation symmetry : if there was one centre of rotation there always seems to be a second centre that also worked. Can you find a design that has only. . . .

Cut Cube

Stage: 5 Challenge Level:

Find the shape and symmetries of the two pieces of this cut cube.

Mean Geometrically

Stage: 5 Challenge Level:

A and B are two points on a circle centre O. Tangents at A and B cut at C. CO cuts the circle at D. What is the relationship between areas of ADBO, ABO and ACBO?

Eight Dominoes

Stage: 2, 3 and 4 Challenge Level:

Using the 8 dominoes make a square where each of the columns and rows adds up to 8

Dicey Decisions

Stage: 5 Challenge Level:

Can you devise a fair scoring system when dice land edge-up or corner-up?

Arclets

Stage: 4 Challenge Level:

Each of the following shapes is made from arcs of a circle of radius r. What is the perimeter of a shape with 3, 4, 5 and n "nodes".

Maltese Cross

Stage: 5 Challenge Level:

Sketch the graph of $xy(x^2 - y^2) = x^2 + y^2$ consisting of four curves and a single point at the origin. Convert to polar form. Describe the symmetries of the graph.

Encircling

Stage: 4 Challenge Level:

An equilateral triangle is sitting on top of a square. What is the radius of the circle that circumscribes this shape?

Flower Power

Stage: 3 and 4 Challenge Level:

Create a symmetrical fabric design based on a flower motif - and realise it in Logo.

More Dicey Decisions

Stage: 5 Challenge Level:

The twelve edge totals of a standard six-sided die are distributed symmetrically. Will the same symmetry emerge with a dodecahedral die?

Tournament Scheduling

Stage: 3, 4 and 5

Scheduling games is a little more challenging than one might desire. Here are some tournament formats that sport schedulers use.

Logosquares

Stage: 5 Challenge Level:

Ten squares form regular rings either with adjacent or opposite vertices touching. Calculate the inner and outer radii of the rings that surround the squares.

Pitchfork

Stage: 5 Challenge Level:

Plot the graph of x^y = y^x in the first quadrant and explain its properties.

Holly

Stage: 4 Challenge Level:

The ten arcs forming the edges of the "holly leaf" are all arcs of circles of radius 1 cm. Find the length of the perimeter of the holly leaf and the area of its surface.

Folium of Descartes

Stage: 5 Challenge Level:

Investigate the family of graphs given by the equation x^3+y^3=3axy for different values of the constant a.

Octa-flower

Stage: 5 Challenge Level:

Join some regular octahedra, face touching face and one vertex of each meeting at a point. How many octahedra can you fit around this point?

Witch of Agnesi

Stage: 5 Challenge Level:

Sketch the members of the family of graphs given by y = a^3/(x^2+a^2) for a=1, 2 and 3.

Classifying Solids Using Angle Deficiency

Stage: 3 and 4 Challenge Level:

Toni Beardon has chosen this article introducing a rich area for practical exploration and discovery in 3D geometry

Cocked Hat

Stage: 5 Challenge Level:

Sketch the graphs for this implicitly defined family of functions.

Square Pizza

Stage: 4 Challenge Level:

Can you show that you can share a square pizza equally between two people by cutting it four times using vertical, horizontal and diagonal cuts through any point inside the square?

Prime Magic

Stage: 2, 3 and 4 Challenge Level:

Place the numbers 1, 2, 3,..., 9 one on each square of a 3 by 3 grid so that all the rows and columns add up to a prime number. How many different solutions can you find?

Sliced

Stage: 4 Challenge Level:

An irregular tetrahedron has two opposite sides the same length a and the line joining their midpoints is perpendicular to these two edges and is of length b. What is the volume of the tetrahedron?