• Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

Maths Cubes Investigation

Extracts from this document...


HIGHER TIER TASK STRUCTURES Rigid structures are constructed using unit rods. An example is shown below. The individual rods in the structures are held together using different types of joints. Some examples are shown below. 3 Joint 4 Joint 5 Joint 6 Joint Investigate structures constructed from unit rods. My Plan I have decided to investigate the number of different joints in cubes. I will draw cubes of dimensions 1x1x1, 2x2x2, 3x3x3, 4x4x4 and 5x5x5. After drawing these cubes and counting the number of different joints, I hope to find a pattern and formula for working out the number of different rods in shapes nxnxn. After finding this formula I will check it against shapes 6x6x6, 7x7x7, 8x8x8, 9x9x9 and 10x10x10, to see if it works. I will then use this theory on more complex shapes like cuboids. Collecting Results To set about collecting my results I drew the cubes on isometric paper and drew the joints in different colours so that it would be easier to count them. ...read more.


On the 1x1x1 cube there aren't any edges as there is only 8 Joints in total and these are the 3 Joints. The amount of 4 Joints increases by 12 for each extra 1 cm� you increase the dimensions by because another joint is added for each edge. The rule for 4 Joints is: 12(n-1). 5 Joints The number of 5 Joints increases in a slightly less obvious pattern than 3 Joints or 4 Joints. The pattern is actually that the number of 5 Joints increases by the following rule: 6(n-1) �. The reason for this is because 5 Joints are found on the faces of the cube. There are six faces on a cube and this explains the 6 in the rule. The reason for the square number is that each time the dimensions are increased by ncm� a square of ncm� is made on the face of the cube. ...read more.


= ab+a Rows + Columns = a+2ab+b Layers- c+1 Total for all layers- (a+2ab+b)(c+1) Vertical Rods For 1 Layer- (b+1)(a+1) Layers- c+1 Total for all Layers- (b+1)(a+1)c Horizontal and Vertical Rods 3abc+2ab+2ac+2bc+a+b+c JOINTS 3 Joints As in a cube there are only ever 8, 3 Joints in a cuboid so again the rule is 3J=8. 4 Joints The rule for 4 Joints is 4(a-1)+4(b-1)+4(c-1). This is relates to the edges of the cuboid. 5 Joints As in the cube, the 5 Joints are found on the faces of the cuboid. The rule for the amount of 5 Joints is this 2(a-1)(b-1)+2(b-1)(c-1)+2(a-1)(c-1). 6 Joints The 6 Joints are again found 'inside' the cube. As the dimensions of the cube are axbxc, then the amount of 6 Joints is (a-1)(b-1)(c-1). Total Joints The rule for the total number of Joints in the cuboid is this (a+1)(b+1)(c+1). This is because this is the equivalent to the cubes formula for total Joints which is (n+1)� Colin Devitt 11L Maths Coursework 1 ...read more.

The above preview is unformatted text

This student written piece of work is one of many that can be found in our GCSE Hidden Faces and Cubes section.

Found what you're looking for?

  • Start learning 29% faster today
  • 150,000+ documents available
  • Just £6.99 a month

Not the one? Search for your essay title...
  • Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

See related essaysSee related essays

Related GCSE Hidden Faces and Cubes essays

  1. An investigation to look at shapes made up of other shapes (starting with triangles, ...

    this new formula works for finding Q - I presume that if I rearrange this to give P= and D=, these two new formulas will work. Q=P/2+D-1 can be rearranged to give P=2(Q-D+1) and D=Q-P/2+1. Although I am pretty sure that these formulas work - as the formula they are

  2. Painted Cube Investigation

    a 1 x 1 x 1, it is impossible to have a cube with 6 painted faces. Extending the Investigation I extended the investigation to cuboids.

  1. Borders Investigation Maths Coursework

    will have 61 white squares and I predict that it will have 24 black squares as the no of black squares seems to go up in multiples of 4 (which means 4 is added is added to every next pattern).

  2. Maths Investigation -Painted Cubes

    As I had now found the formulas, I could predict the numbers of faces for the original question... For a cube sized 20 x 20 x 20... The number of cubes with three faces painted will be 8. The number of cubes with two faces painted will be 216.

  1. shapes investigation coursework

    Also, I do not have to worry about the value of (T+2-P)/2 being anything other than a whole number (i.e. when T-P gives an odd number, then /2 to give x.5). This is because when T is an even number, P is an even number, so T+P is therefore an even number.

  2. With Close Reference to The Wasteland and the Great Gatsby Compare and Contrast how ...

    # & I was standing beside his bed and he was sitting up between the sheets, clad in his underwear, with a great portfolio in his hands (Chapter 2) # I had no girl whose disembodied face floated along the dark cornices and blinding signs, and so I drew up the girl beside me, tightening my arms (Chapter 4)

  1. The Painted Cube - Maths Investigations

    To find out the formulae for 1 face covered in paint I first worked out the total surface area of the cubes in the large cube, which gave me 2(LH+LW+WH). A LH gives me the blue, a LW gives me the red and WH gives me the green.

  2. Cubes and Cuboids Investigation.

    be 6 similar squares with the same amount of cubes with one face painted and so the formula for cubes with only one painted face is Y=(X-2)2*6. 'font-size:14.0pt; '>The last formula that must be found out to make the set complete is that which tells us the number of cubes with no painted faces.

  • Over 160,000 pieces
    of student written work
  • Annotated by
    experienced teachers
  • Ideas and feedback to
    improve your own work