Resources tagged with: Visualising

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There are 101 results

Broad Topics > Using, Applying and Reasoning about Mathematics > Visualising

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Efficient Packing

Age 14 to 16 Challenge Level:

How efficiently can you pack together disks?

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Escriptions

Age 16 to 18 Challenge Level:

For any right-angled triangle find the radii of the three escribed circles touching the sides of the triangle externally.

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Like a Circle in a Spiral

Age 7 to 16 Challenge Level:

A cheap and simple toy with lots of mathematics. Can you interpret the images that are produced? Can you predict the pattern that will be produced using different wheels?

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Rolling Coins

Age 14 to 16 Challenge Level:

A blue coin rolls round two yellow coins which touch. The coins are the same size. How many revolutions does the blue coin make when it rolls all the way round the yellow coins? Investigate for a. . . .

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Star Gazing

Age 14 to 16 Challenge Level:

Find the ratio of the outer shaded area to the inner area for a six pointed star and an eight pointed star.

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LOGO Challenge - Circles as Animals

Age 11 to 16 Challenge Level:

See if you can anticipate successive 'generations' of the two animals shown here.

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Ford Circles

Age 16 to 18 Challenge Level:

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

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Tilting Triangles

Age 14 to 16 Challenge Level:

A right-angled isosceles triangle is rotated about the centre point of a square. What can you say about the area of the part of the square covered by the triangle as it rotates?

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A Rolling Disc - Periodic Motion

Age 16 to 18

Imagine a rectangular tray lying flat on a table. Suppose that a plate lies on the tray and rolls around, in contact with the sides as it rolls. What can we say about the motion?

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All Tied Up

Age 14 to 16 Challenge Level:

A ribbon runs around a box so that it makes a complete loop with two parallel pieces of ribbon on the top. How long will the ribbon be?

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Doesn't Add Up

Age 14 to 16 Challenge Level:

In this problem we are faced with an apparently easy area problem, but it has gone horribly wrong! What happened?

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Circles Ad Infinitum

Age 16 to 18 Challenge Level:

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?

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Tied Up

Age 14 to 16 Short Challenge Level:

How much of the field can the animals graze?

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Set Square

Age 16 to 18 Challenge Level:

A triangle PQR, right angled at P, slides on a horizontal floor with Q and R in contact with perpendicular walls. What is the locus of P?

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Coke Machine

Age 14 to 16 Challenge Level:

The coke machine in college takes 50 pence pieces. It also takes a certain foreign coin of traditional design...

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Corridors

Age 14 to 16 Challenge Level:

A 10x10x10 cube is made from 27 2x2 cubes with corridors between them. Find the shortest route from one corner to the opposite corner.

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Bendy Quad

Age 14 to 16 Challenge Level:

Four rods are hinged at their ends to form a convex quadrilateral. Investigate the different shapes that the quadrilateral can take. Be patient this problem may be slow to load.

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Classic Cube

Age 16 to 18 Challenge Level:

The net of a cube is to be cut from a sheet of card 100 cm square. What is the maximum volume cube that can be made from a single piece of card?

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Just Rolling Round

Age 14 to 16 Challenge Level:

P is a point on the circumference of a circle radius r which rolls, without slipping, inside a circle of radius 2r. What is the locus of P?

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Steel Cables

Age 14 to 16 Challenge Level:

Some students have been working out the number of strands needed for different sizes of cable. Can you make sense of their solutions?

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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?

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Contact

Age 14 to 16 Challenge Level:

A circular plate rolls in contact with the sides of a rectangular tray. How much of its circumference comes into contact with the sides of the tray when it rolls around one circuit?

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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?

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Three Cubes

Age 14 to 16 Challenge Level:

Can you work out the dimensions of the three cubes?

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When the Angles of a Triangle Don't Add up to 180 Degrees

Age 14 to 18

This article outlines the underlying axioms of spherical geometry giving a simple proof that the sum of the angles of a triangle on the surface of a unit sphere is equal to pi plus the area of the. . . .

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The Spider and the Fly

Age 14 to 16 Challenge Level:

A spider is sitting in the middle of one of the smallest walls in a room and a fly is resting beside the window. What is the shortest distance the spider would have to crawl to catch the fly?

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Semi-regular Tessellations

Age 11 to 16 Challenge Level:

Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?

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Sliding Puzzle

Age 11 to 16 Challenge Level:

The aim of the game is to slide the green square from the top right hand corner to the bottom left hand corner in the least number of moves.

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Jam

Age 14 to 16 Challenge Level:

A game for 2 players

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Double Trouble

Age 14 to 16 Challenge Level:

Simple additions can lead to intriguing results...

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Painted Cube

Age 14 to 16 Challenge Level:

Imagine a large cube made from small red cubes being dropped into a pot of yellow paint. How many of the small cubes will have yellow paint on their faces?

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One and Three

Age 14 to 16 Challenge Level:

Two motorboats travelling up and down a lake at constant speeds leave opposite ends A and B at the same instant, passing each other, for the first time 600 metres from A, and on their return, 400. . . .

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Mach Attack

Age 16 to 18 Challenge Level:

Have you got the Mach knack? Discover the mathematics behind exceeding the sound barrier.

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Wrapping Gifts

Age 16 to 18 Challenge Level:

A box of size a cm by b cm by c cm is to be wrapped with a square piece of wrapping paper. Without cutting the paper what is the smallest square this can be?

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Fitting Flat Shapes

Age 16 to 18 Challenge Level:

How efficiently can various flat shapes be fitted together?

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Mystic Rose

Age 14 to 16 Challenge Level:

Use the animation to help you work out how many lines are needed to draw mystic roses of different sizes.

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Baravelle

Age 7 to 16 Challenge Level:

What can you see? What do you notice? What questions can you ask?

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Cuboid Challenge

Age 11 to 16 Challenge Level:

What's the largest volume of box you can make from a square of paper?

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Air Nets

Age 7 to 18 Challenge Level:

Can you visualise whether these nets fold up into 3D shapes? Watch the videos each time to see if you were correct.

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Packing 3D Shapes

Age 14 to 16 Challenge Level:

What 3D shapes occur in nature. How efficiently can you pack these shapes together?

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Partly Painted Cube

Age 14 to 16 Challenge Level:

Jo made a cube from some smaller cubes, painted some of the faces of the large cube, and then took it apart again. 45 small cubes had no paint on them at all. How many small cubes did Jo use?

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Clocking Off

Age 7 to 16 Challenge Level:

I found these clocks in the Arts Centre at the University of Warwick intriguing - do they really need four clocks and what times would be ambiguous with only two or three of them?

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Triangles Within Triangles

Age 14 to 16 Challenge Level:

Can you find a rule which connects consecutive triangular numbers?

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Shaping the Universe I - Planet Earth

Age 11 to 16

This article explores ths history of theories about the shape of our planet. It is the first in a series of articles looking at the significance of geometric shapes in the history of astronomy.

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Triangles in the Middle

Age 11 to 18 Challenge Level:

This task depends on groups working collaboratively, discussing and reasoning to agree a final product.

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AMGM

Age 14 to 16 Challenge Level:

Can you use the diagram to prove the AM-GM inequality?

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Building Gnomons

Age 14 to 16 Challenge Level:

Build gnomons that are related to the Fibonacci sequence and try to explain why this is possible.

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Triangles Within Pentagons

Age 14 to 16 Challenge Level:

Show that all pentagonal numbers are one third of a triangular number.

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Speeding Boats

Age 14 to 16 Challenge Level:

Two boats travel up and down a lake. Can you picture where they will cross if you know how fast each boat is travelling?

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Triangles Within Squares

Age 14 to 16 Challenge Level:

Can you find a rule which relates triangular numbers to square numbers?