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#### Resources tagged with Regular polygons and circles similar to Sweets in a Box:

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### There are 54 results

Broad Topics > Angles, Polygons, and Geometrical Proof > Regular polygons and circles

### Sweets in a Box

##### Stage: 2 Challenge Level:

How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?

### Round and Round the Circle

##### Stage: 2 Challenge Level:

What happens if you join every second point on this circle? How about every third point? Try with different steps and see if you can predict what will happen.

### Shapes on the Playground

##### Stage: 2 Challenge Level:

Sally and Ben were drawing shapes in chalk on the school playground. Can you work out what shapes each of them drew using the clues?

### Egyptian Rope

##### Stage: 2 Challenge Level:

The ancient Egyptians were said to make right-angled triangles using a rope with twelve equal sections divided by knots. What other triangles could you make if you had a rope like this?

### Bracelets

##### Stage: 2 Challenge Level:

Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?

### Shaping Up

##### Stage: 2 Challenge Level:

Are all the possible combinations of two shapes included in this set of 27 cards? How do you know?

### Shedding Some Light

##### Stage: 2 Challenge Level:

Make an estimate of how many light fittings you can see. Was your estimate a good one? How can you decide?

### Shaping It

##### Stage: 1 and 2 Challenge Level:

These pictures were made by starting with a square, finding the half-way point on each side and joining those points up. You could investigate your own starting shape.

### Hexagon Transformations

##### Stage: 2 Challenge Level:

Can you cut a regular hexagon into two pieces to make a parallelogram? Try cutting it into three pieces to make a rhombus!

### Where Are They?

##### Stage: 2 Challenge Level:

Use the isometric grid paper to find the different polygons.

### Part the Polygons

##### Stage: 2 Short Challenge Level:

Draw three straight lines to separate these shapes into four groups - each group must contain one of each shape.

### Triangular Hexagons

##### Stage: 2 Challenge Level:

Investigate these hexagons drawn from different sized equilateral triangles.

### Circle Panes

##### Stage: 2 Challenge Level:

Look at the mathematics that is all around us - this circular window is a wonderful example.

### Overlapping Circles

##### Stage: 2 Challenge Level:

What shaped overlaps can you make with two circles which are the same size? What shapes are 'left over'? What shapes can you make when the circles are different sizes?

### Cube Paths

##### Stage: 3 Challenge Level:

Given a 2 by 2 by 2 skeletal cube with one route `down' the cube. How many routes are there from A to B?

### Sports Equipment

##### Stage: 2 Challenge Level:

If these balls are put on a line with each ball touching the one in front and the one behind, which arrangement makes the shortest line of balls?

### LOGO Challenge 9 - Overlapping Polygons

##### Stage: 2, 3 and 4 Challenge Level:

This LOGO challenge starts by looking at 10-sided polygons then generalises the findings to any polygon, putting particular emphasis on external angles

### Tessellation Interactivity

##### Stage: 2, 3 and 4 Challenge Level:

An environment that enables you to investigate tessellations of regular polygons

### Overlapping Again

##### Stage: 2 Challenge Level:

What shape is the overlap when you slide one of these shapes half way across another? Can you picture it in your head? Use the interactivity to check your visualisation.

### LOGO Challenge 11 - More on Circles

##### Stage: 3 and 4 Challenge Level:

Thinking of circles as polygons with an infinite number of sides - but how does this help us with our understanding of the circumference of circle as pi x d? This challenge investigates. . . .

### LOGO Challenge 1 - Star Square

##### Stage: 2, 3 and 4 Challenge Level:

Can you use LOGO to create this star pattern made from squares. Only basic LOGO knowledge needed.

### A Chordingly

##### Stage: 3 Challenge Level:

Find the area of the annulus in terms of the length of the chord which is tangent to the inner circle.

### Hex

##### Stage: 3 Challenge Level:

Explain how the thirteen pieces making up the regular hexagon shown in the diagram can be re-assembled to form three smaller regular hexagons congruent to each other.

### Yin Yang

##### Stage: 2 Challenge Level:

Can you reproduce the Yin Yang symbol using a pair of compasses?

### Intersecting Circles

##### Stage: 3 Challenge Level:

Three circles have a maximum of six intersections with each other. What is the maximum number of intersections that a hundred circles could have?

### Rolling Around

##### Stage: 3 Challenge Level:

A circle rolls around the outside edge of a square so that its circumference always touches the edge of the square. Can you describe the locus of the centre of the circle?

### LOGO Challenge 10 - Circles

##### Stage: 3 and 4 Challenge Level:

In LOGO circles can be described in terms of polygons with an infinite (in this case large number) of sides - investigate this definition further.

### Like a Circle in a Spiral

##### Stage: 2, 3 and 4 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?

### LOGO Challenge 6 - Triangles and Stars

##### Stage: 3 and 4 Challenge Level:

Recreating the designs in this challenge requires you to break a problem down into manageable chunks and use the relationships between triangles and hexagons. An exercise in detail and elegance.

### LOGO Challenge 12 - Concentric Circles

##### Stage: 3 and 4 Challenge Level:

Can you reproduce the design comprising a series of concentric circles? Test your understanding of the realtionship betwwn the circumference and diameter of a circle.

### Opposite Vertices

##### Stage: 3 Challenge Level:

Can you recreate squares and rhombuses if you are only given a side or a diagonal?

### Shogi Shapes

##### Stage: 3 Challenge Level:

Shogi tiles can form interesting shapes and patterns... I wonder whether they fit together to make a ring?

### LOGO Challenge - Circles as Animals

##### Stage: 3 and 4 Challenge Level:

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

### Arclets Explained

##### Stage: 3 and 4

This article gives an wonderful insight into students working on the Arclets problem that first appeared in the Sept 2002 edition of the NRICH website.

### Shapely Tiling

##### Stage: 2 Challenge Level:

Use the interactivity to make this Islamic star and cross design. Can you produce a tessellation of regular octagons with two different types of triangle?

##### Stage: 2 and 3 Challenge Level:

What shape and size of drinks mat is best for flipping and catching?

### Square Pegs

##### Stage: 3 Challenge Level:

Which is a better fit, a square peg in a round hole or a round peg in a square hole?

### Clock Hands

##### Stage: 2 Challenge Level:

This investigation explores using different shapes as the hands of the clock. What things occur as the the hands move.

### First Forward Into Logo 2: Polygons

##### Stage: 2, 3 and 4 Challenge Level:

This is the second in a twelve part introduction to Logo for beginners. In this part you learn to draw polygons.

### Squaring the Circle

##### Stage: 3 Challenge Level:

Bluey-green, white and transparent squares with a few odd bits of shapes around the perimeter. But, how many squares are there of each type in the complete circle? Study the picture and make. . . .

### The Pi Are Square

##### Stage: 3 Challenge Level:

A circle with the radius of 2.2 centimetres is drawn touching the sides of a square. What area of the square is NOT covered by the circle?

### Not So Little X

##### Stage: 3 Challenge Level:

Two circles are enclosed by a rectangle 12 units by x units. The distance between the centres of the two circles is x/3 units. How big is x?

### Pie Cuts

##### Stage: 3 Challenge Level:

Investigate the different ways of cutting a perfectly circular pie into equal pieces using exactly 3 cuts. The cuts have to be along chords of the circle (which might be diameters).

### F'arc'tion

##### Stage: 3 Challenge Level:

At the corner of the cube circular arcs are drawn and the area enclosed shaded. What fraction of the surface area of the cube is shaded? Try working out the answer without recourse to pencil and. . . .

### Bull's Eye

##### Stage: 3 Challenge Level:

What fractions of the largest circle are the two shaded regions?

### Floored

##### Stage: 3 Challenge Level:

A floor is covered by a tessellation of equilateral triangles, each having three equal arcs inside it. What proportion of the area of the tessellation is shaded?

### The Pillar of Chios

##### Stage: 3 Challenge Level:

Semicircles are drawn on the sides of a rectangle ABCD. A circle passing through points ABCD carves out four crescent-shaped regions. Prove that the sum of the areas of the four crescents is equal to. . . .

##### Stage: 2, 3 and 4 Challenge Level:

A metal puzzle which led to some mathematical questions.

### Lighting up Time

##### Stage: 2 and 3 Challenge Level:

A very mathematical light - what can you see?

### Coins on a Plate

##### Stage: 3 Challenge Level:

Points A, B and C are the centres of three circles, each one of which touches the other two. Prove that the perimeter of the triangle ABC is equal to the diameter of the largest circle.