# Resources tagged with: Symmetry

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### There are 34 results

Broad Topics > Transformations and constructions > Symmetry

### 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?

### 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

### 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?

### 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?

### 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?

### 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?

### 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?

### 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?

### Cocked Hat

##### Age 16 to 18 Challenge Level:

Sketch the graphs for this implicitly defined family of functions.

### 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?

### 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?

### 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.

### 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.

### 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.

### 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.

### Cut Cube

##### Age 16 to 18 Challenge Level:

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

### 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?

### 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.

### 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.

### Dicey Decisions

##### Age 16 to 18 Challenge Level:

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

### Rose

##### Age 16 to 18 Challenge Level:

What groups of transformations map a regular pentagon to itself?

### Trominoes

##### Age 11 to 16 Challenge Level:

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

### Pitchfork

##### Age 16 to 18 Challenge Level:

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

### 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.

### Symmetric Trace

##### Age 14 to 16 Challenge Level:

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

### 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.

### 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

### 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?

### 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

### 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".

### 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. . . .

### 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.

### Flower Power

##### Age 11 to 16 Challenge Level:

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