Visualising - advanced

Investigate how networks can be used to solve a problem for the 18th Century inhabitants of Konigsberg.

Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.

Infographics are a powerful way of communicating statistical information. Can you come up with your own?

How can you decide if a graph is traversable?

Starting with two basic vector steps, which destinations can you reach on a vector walk?

This problem challenges you to sketch curves with different properties.

Charlie likes to go for walks around a square park, while Alison likes to cut across diagonally. Can you find relationships between the vectors they walk along?

Watch the video to see how to sum the sequence. Can you adapt the method to sum other sequences?

Can you work out which spinners were used to generate the frequency charts?

10 graphs of experimental data are given. Can you use a spreadsheet to find algebraic graphs which match them closely, and thus discover the formulae most likely to govern the underlying processes?

Take a triangular number, multiply it by 8 and add 1. What is special about your answer? Can you prove it?

Find the sum of this series of surds.

Show that if you add 1 to the product of four consecutive numbers the answer is ALWAYS a perfect square.

Can you work out which processes are represented by the graphs?

Some treasure has been hidden in a three-dimensional grid! Can you work out a strategy to find it as efficiently as possible?

Can you make sense of the three methods to work out what fraction of the total area is shaded?

Which curve is which, and how would you plan a route to pass between them?

If you know some points on a line, can you work out other points in between?

Which line graph, equations and physical processes go together?

Go on a vector walk and determine which points on the walk are closest to the origin.

This is a beautiful result involving a parabola and parallels.

Is this surd sum exactly 3?

Consider these analogies for helping to understand key concepts in calculus.

Investigate the relationship between speeds recorded and the distance travelled in this kinematic scenario.

There are many different methods to solve this geometrical problem - how many can you find?

This problem asks you to use your curve sketching knowledge to find all the solutions to an equation.

A circle is inscribed in an equilateral triangle. Smaller circles touch it and the sides of the triangle, the process continuing indefinitely. What is the sum of the areas of all the circles?

Discover how networks can be used to prove Euler's Polyhedron formula.

The famous film star Birkhoff Maclane wants to reach her refreshing drink. Should she run around the pool or swim across?

Do you have enough information to work out the area of the shaded quadrilateral?

Given any three non intersecting circles in the plane find another circle or straight line which cuts all three circles orthogonally.

Explore the hyperbolic functions sinh and cosh using what you know about the exponential function.

Stick some cubes together to make a cuboid. Find two of the angles by as many different methods as you can devise.

Draw graphs of the sine and modulus functions and explain the humps.

Match the descriptions of physical processes to these differential equations.

Can you find the link between these beautiful circle patterns and Farey Sequences?

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

Can you make a curve to match my friend's requirements?