# Resources tagged with: Visualising

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### There are 102 results

Broad Topics > Thinking Mathematically > Visualising

### Middle Man

##### Age 16 to 18Challenge Level

Mark a point P inside a closed curve. Is it always possible to find two points that lie on the curve, such that P is the mid point of the line joining these two points?

### Yih or Luk Tsut K'i or Three Men's Morris

##### Age 11 to 18Challenge Level

Some puzzles requiring no knowledge of knot theory, just a careful inspection of the patterns. A glimpse of the classification of knots and a little about prime knots, crossing numbers and. . . .

### Proofs with Pictures

##### Age 14 to 18

Some diagrammatic 'proofs' of algebraic identities and inequalities.

### The Bridges of Konigsberg

##### Age 11 to 18Challenge Level

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

### Triangles Within Triangles

##### Age 14 to 16Challenge Level

Can you find a rule which connects consecutive triangular numbers?

### Triangles Within Pentagons

##### Age 14 to 16Challenge Level

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

### Maximum Scattering

##### Age 16 to 18Challenge Level

Your data is a set of positive numbers. What is the maximum value that the standard deviation can take?

### Prime Magic

##### Age 7 to 16Challenge 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?

### Three Cubes

##### Age 14 to 16Challenge Level

Can you work out the dimensions of the three cubes?

### Sliced

##### Age 14 to 16Challenge 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?

### Triangles Within Squares

##### Age 14 to 16Challenge Level

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

### Classical Means

##### Age 16 to 18Challenge Level

Use the diagram to investigate the classical Pythagorean means.

### Proximity

##### Age 14 to 16Challenge Level

We are given a regular icosahedron having three red vertices. Show that it has a vertex that has at least two red neighbours.

### Problem Solving, Using and Applying and Functional Mathematics

##### Age 5 to 18Challenge Level

Problem solving is at the heart of the NRICH site. All the problems give learners opportunities to learn, develop or use mathematical concepts and skills. Read here for more information.

### Fermat's Poser

##### Age 14 to 16Challenge Level

Find the point whose sum of distances from the vertices (corners) of a given triangle is a minimum.

### Painted Cube

##### Age 14 to 16Challenge 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?

### One and Three

##### Age 14 to 16Challenge 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. . . .

### The Spider and the Fly

##### Age 14 to 16Challenge 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?

### AMGM

##### Age 14 to 16Challenge Level

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

### All Tied Up

##### Age 14 to 16Challenge 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?

### Jam

##### Age 14 to 16Challenge Level

A game for 2 players

### Around and Back

##### Age 14 to 16Challenge Level

A cyclist and a runner start off simultaneously around a race track each going at a constant speed. The cyclist goes all the way around and then catches up with the runner. He then instantly turns. . . .

### Tilting Triangles

##### Age 14 to 16Challenge 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?

### Wari

##### Age 14 to 16Challenge Level

This is a simple version of an ancient game played all over the world. It is also called Mancala. What tactics will increase your chances of winning?

### Inside Out

##### Age 14 to 16Challenge Level

There are 27 small cubes in a 3 x 3 x 3 cube, 54 faces being visible at any one time. Is it possible to reorganise these cubes so that by dipping the large cube into a pot of paint three times you. . . .

### Corridors

##### Age 14 to 16Challenge 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.

### Changing Places

##### Age 14 to 16Challenge Level

Place a red counter in the top left corner of a 4x4 array, which is covered by 14 other smaller counters, leaving a gap in the bottom right hand corner (HOME). What is the smallest number of moves. . . .

### Cuboid Challenge

##### Age 11 to 16Challenge Level

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

### Steel Cables

##### Age 14 to 16Challenge Level

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

### Partly Painted Cube

##### Age 14 to 16Challenge 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?

### Mystic Rose

##### Age 14 to 16Challenge Level

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

### Speeding Boats

##### Age 14 to 16Challenge 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?

### Summing Squares

##### Age 14 to 16Challenge Level

Discover a way to sum square numbers by building cuboids from small cubes. Can you picture how the sequence will grow?

### Air Nets

##### Age 7 to 18Challenge Level

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

### Circuit Training

##### Age 14 to 16Challenge Level

Mike and Monisha meet at the race track, which is 400m round. Just to make a point, Mike runs anticlockwise whilst Monisha runs clockwise. Where will they meet on their way around and will they ever. . . .

### Clocking Off

##### Age 7 to 16Challenge 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?

### The Development of Spatial and Geometric Thinking: 5 to 18

##### Age 5 to 16

This is the first article in a series which aim to provide some insight into the way spatial thinking develops in children, and draw on a range of reported research. The focus of this article is the. . . .

### Sprouts

##### Age 11 to 16Challenge Level

A game for 2 people. Take turns joining two dots, until your opponent is unable to move.

### Building Gnomons

##### Age 14 to 16Challenge Level

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

### Square It

##### Age 11 to 16Challenge Level

Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.

### Sliding Puzzle

##### Age 11 to 16Challenge 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.

### Hypotenuse Lattice Points

##### Age 14 to 16Challenge Level

The triangle OMN has vertices on the axes with whole number co-ordinates. How many points with whole number coordinates are there on the hypotenuse MN?

### Vanishing Point

##### Age 14 to 18Challenge Level

How can visual patterns be used to prove sums of series?

### Platonic Planet

##### Age 14 to 16Challenge Level

Glarsynost lives on a planet whose shape is that of a perfect regular dodecahedron. Can you describe the shortest journey she can make to ensure that she will see every part of the planet?

### Thinking Through, and By, Visualising

##### Age 7 to 16

This article is based on some of the ideas that emerged during the production of a book which takes visualising as its focus. We began to identify problems which helped us to take a structured view. . . .

### Building Tetrahedra

##### Age 14 to 16Challenge Level

Can you make a tetrahedron whose faces all have the same perimeter?

### Picture Story

##### Age 14 to 16Challenge Level

Can you see how this picture illustrates the formula for the sum of the first six cube numbers?

### Natural Sum

##### Age 14 to 16Challenge Level

The picture illustrates the sum 1 + 2 + 3 + 4 = (4 x 5)/2. Prove the general formula for the sum of the first n natural numbers and the formula for the sum of the cubes of the first n natural. . . .

### Making Tracks

##### Age 14 to 16Challenge Level

A bicycle passes along a path and leaves some tracks. Is it possible to say which track was made by the front wheel and which by the back wheel?