Resources tagged with: Symmetry

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There are 34 results

Broad Topics > Transformations and constructions > Symmetry

Cocked Hat

Age 16 to 18
Challenge Level

Sketch the graphs for this implicitly defined family of functions.

Maltese Cross

Age 16 to 18
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.

Folium of Descartes

Age 16 to 18
Challenge Level

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

Pitchfork

Age 16 to 18
Challenge Level

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

Witch of Agnesi

Age 16 to 18
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.

More Dicey Decisions

Age 16 to 18
Challenge Level

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

Octa-flower

Age 16 to 18
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?

Cut Cube

Age 16 to 18
Challenge Level

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

Mean Geometrically

Age 16 to 18
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?

Prime Magic

Age 7 to 16
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?

Trominoes

Age 11 to 16
Challenge Level

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

Rose

Age 16 to 18
Challenge Level

What groups of transformations map a regular pentagon to itself?

Dicey Decisions

Age 16 to 18
Challenge Level

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

Sliced

Age 14 to 16
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?

Holly

Age 14 to 16
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.

Tournament Scheduling

Age 11 to 16

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

Attractive Tablecloths

Age 14 to 16
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?

Two Triangles in a Square

Age 14 to 16
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.

The Frieze Tree

Age 11 to 16

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

Square Pizza

Age 14 to 16
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?

Classifying Solids Using Angle Deficiency

Age 11 to 16
Challenge Level

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

Encircling

Age 14 to 16
Challenge Level

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

Eight Dominoes

Age 7 to 16
Challenge Level

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

Flower Power

Age 11 to 16
Challenge Level

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

A Problem of Time

Age 14 to 16
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?

Arclets

Age 14 to 16
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".

Frieze Patterns in Cast Iron

Age 11 to 16

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

A Roll of Patterned Paper

Age 14 to 16
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

Symmetric Trace

Age 14 to 16
Challenge Level

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

One Reflection Implies Another

Age 14 to 16
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. . . .

Rotations Are Not Single Round Here

Age 14 to 16
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. . . .

Dancing with Maths

Age 7 to 16

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?

Paint Rollers for Frieze Patterns.

Age 11 to 16

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

Logosquares

Age 16 to 18
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.