Resources tagged with Symmetry similar to An Introduction to Galois Theory:
Other tags that relate to An Introduction to Galois Theory
Interactivities. Galois theory. Permutations. Roots of polynomial equations. Structures of simple finite groups. Symmetry. Inverses. Groups. Subgroups. Small software.There are 30 results
Dancing with Maths
Stage: 2, 3, 4 and 5
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?
Frieze Patterns in Cast Iron
Stage: 4 and 5
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
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?
Symmetric Trace
Stage: 4 Challenge Level:
Points off a rolling wheel make traces. What makes those traces have symmetry?
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?
A Resource to Support Work on Transformations
Stage: 4 Challenge Level:
This resources contains a series of interactivities designed to support work on transformations at Key Stage 4.
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. . . .
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. . . .
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?
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.
Plex
Stage: 2, 3, 4 and 5 Challenge Level:
Plex lets you specify a mapping between points and their images. Then you can draw and see the transformed image.
Classifying Solids Using Angle Deficiency
Stage: 3 and 4
Toni Beardon has chosen this article introducing a rich area for practical exploration and discovery in 3D geometry
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?
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.
Trominoes
Stage: 3 and 4 Challenge Level:
Can all but one square of an 8 by 8 Chessboard be covered by Trominoes?
Cut Cube
Stage: 5 Challenge Level:
P, Q and R are points of trisection of 3 non-intersecting perpendicular edges of a cube. Where does the plane PQR cut the other edges of the cube? Describe the symmetries of the 'half cube' obtained.
Pitchfork
Stage: 5 Challenge Level:
Plot the graph of x^y = y^x in the first quadrant and explain its properties.
The Frieze Tree
Stage: 4
Patterns that repeat in a line are strangely interesting. How many types are there and how do you tell one type from another?
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?
Cocked Hat
Stage: 5 Challenge Level:
A new solution to a Tough Nut problem. Aleksander has drawn graphs for members of the family of functions given by the implicit equation (x^2 + 2ay -a^2)^2 = y^2(a^2 - x^2) corresponding to different. . . .
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.
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.
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.
Kissing
Stage: 5 Challenge Level:
Two perpendicular lines are tangential to two identical circles that touch. How big is the circle that just fits between the two lines and the two circles and how would you construct it?
Magical Maze - 35 Activities
Stage: 4 and 5
Investigations and activities for you to enjoy on pattern in nature.
Magical Maze - Lecture Summary
Stage: 4 and 5
An introduction to Ian Stewart's RI Christmas Lectures on Mathematics and Nature with investigations and activities on mathematical patterns in cosmology, music, snowflakes, and flowers, animal. . . .
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?
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.
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