Hidden Faces
Hidden Faces Coursework A cube a total of 6 sides, when it is places on a surface only 5 of the 6 faces can be seen. However if you place 5 cubes side by side, there is a total of 30 faces, but out of this 30 only 17 can be seen. In this coursework I will be finding out the Hidden Faces Coursework A cube a total of 6 sides, when it is places on a surface only 5 of the 6 faces can be seen. However if you place 5 cubes side by side, there is a total of 30 faces, but out of this 30 only 17 can be seen. In this coursework I will be finding out the global formula for the total number of hidden faces for any number of cubes in any way positioned. To find this out I will be testing various numbers of cubes in different positions. This will enable me to find out several different formulae. Using the formulas found I will then be able to find out the global formula. I am generating only 3 formulae to get to the global formula. row 6 faces cube 1 hidden face row 12 faces 2 cubes 4 hidden faces row 18 faces 3 cubes 7 hidden faces row 24 faces 4 cubes 10 hidden faces row 30 faces 5 cubes 13 hidden faces row 36 faces 6 cubes 16 hidden faces row 42 faces 7 cubes 19 hidden faces row 48 faces 8 cubes 22 hidden faces From the cubes drawn above I can see a pattern being formed. The number of hidden faces goes up by 3 every time a cube is added on the
Hidden faces
Introduction My investigation is to find out the number of hidden faces when x amount of cubes are placed on a table. E.g. 1 cube 6 faces 5 faces visible 1 face hidden Number Visible faces Hidden faces 5 2 8 4 3 1 7 4 4 0 5 7 3 6 20 6 7 23 29 8 26 22 9 25 29 0 28 32 It is clear from the table that there is a common pattern apparent in both the progression of visible faces and the progression of hidden faces. In fact both share the same pattern in that they both progress by 3 with each addition of a block. Finding the Nth term From this pattern and from the table I make the formula for the progression of visible faces: 3n + 2 e.g. Number of cubes = 2 Number of visible faces = 2 2 x 3 = 6 + 2 = 8 = 3n + 2 I have proved that this formula works by calculating the 9th and 10th terms by using it. From the pattern and from the table I make the formula for the progression of hidden faces: 3n - 2 e.g. Number of cubes = 2 Number of hidden faces = 4 2 x 3 = 6 - 2 = 4 = 3n - 2 I have proved that this formula works by finding the 9th and 10th terms by using it. Alternative method An alternative way of working out the hidden number of hidden faces is to gather the number of visible faces and subtract that number from the original amount of faces. e.g. 2 cubes Total number of faces
Hidden faces
Hidden faces Introduction I am investigating the number of hidden faces for different rows of cubes. When the cubes are placed on a table, you cannot touch them or move them however you may move the table around. Examples When a cube is placed on a table only 5 of the faces can be seen. So 1 face is hidden. Figure 1 on the dotted paper shows this. When five cubes are placed on a table only 17 faces can be seen. So 13 faces are hidden. Figure 2 on the dotted paper shows this. Part 1 I will tackle this problem by investigating different numbers of cubes. These cubes that I'll be using are 1 cube, 2 cubes, 3 cubes, 4 cubes and 5 cubes. These cubes are shown on the dotted paper. This method is sensible because using the number of cubes I'd be using could lead to finding a formula easily. Number of cubes Number of faces seen Number of faces hidden Total number of faces 5 6 2 8 4 2 3 1 7 8 4 4 0 24 5 7 3 30 Patterns Patterns that I noticed was in the column 'Number of faces seen' that when a cube has 5 faces seen, 2 cubes has 8 faces seen. Three cubes have 11 faces seen, 4 cubes have 14 faces seen and 5 cubes has 17 faces seen. Between each cube is a gap of 3. This could help me with my finding of a formula. I also noticed that in the column 'Number of faces hidden' that when a cube has 1 face hidden, 2 cubes have 4 faces hidden. Three cubes have 7
Hidden Faces.
Mathematics- Hidden Faces Coursework Aim My aim is to find out different formulas for the number of 'hidden faces', including the global formula. It should consist of simple and understandable explanations with examples. Prediction * I predict that I will be able to find out the global and including others * I also predict that there will be a good and understandable relationship with the number of hidden faces and seen faces to give me the total number of faces. Procedure No. of cubes Hidden faces Seen faces Total no. of faces 5 6 2 4 8 2 3 7 1 8 4 0 4 24 5 3 7 30 6 6 20 36 7 9 23 42 8 21 26 48 Nth term 2 3 4 5 6 7 8 Hidden Face 4 7 0 3 6 9 21 Difference +3 +3 +3 +3 +3 +3 +3 +3 Nth term 2 3 4 5 6 7 8 Seen Face 5 8 1 4 7 20 23 26 Difference +3 +3 +3 +3 +3 +3 +3 +3 Nth term 2 3 4 5 6 7 8 Total No. of Faces 6 2 8 24 30 36 42 48 Difference +6 +6 +6 +6 +6 +6 +6 +6 Linear Equation Y = mx + c Nth = mn + c Nth = 3n = 3n- 2 I will now use the linear rule on the results above (hidden Faces), I will see if I could find the global formula that will work on any number of cubes in a row. The sequence goes up in 3's, So m = 3 Nth = 3n So c = -2 FORMULA CHECK 3n - 2 3 × 10 - 2 =28 This shows that the formula is correct. I now know that the formula works
Hidden faces investigation.
Hidden Faces Investigation Introduction I am going to investigate the number of hidden faces when cubes are joined together. The aim of this task is to find a formula, which is common with every cube and hidden face. I will be using multi-link for this investigation. First I will see how many hidden faces are on 1 cube and carry on until I reach up to 6 cubes. One cube has one hidden face and it is the one that is on the table. When there is more than one cube there will also be 2 or more hidden faces where they join together. Hidden Face is here underneath the cube, the face that is on the table. Prediction I predict that with 1 cube there will be 1 hidden face and this face is faced down to the table, but because I have to add cubes to the row each time the number of hidden faces will increase, so will the showing faces and the faces altogether. I think that every time a cube is added to the row the amount of hidden faces will rise by 3 every time. Results The nth term of the sequence is 3n - 2 = Hidden face. I have done 7 cubes, now with this formula I can find out how many hidden faces there are on 8 cubes. 3n - 2 = Hidden faces 3x (8) - 2 24 - 2 = 22 This shows us that there will be 22 hidden faces on 8 cubes. Conclusion My results show that my prediction was correct. You do need to add 3 each time a cube is added and the
I am doing an investigation to look at shapes made up of other shapes.
I am doing an investigation to look at shapes made up of other shapes (starting with triangles, then going on squares and hexagons. I will try to find the relationship between the perimeter (in cm), dots enclosed and the amount of shapes (i.e. triangles etc.) used to make a shape. From this, I will try to find a formula linking P (perimeter), D (dots enclosed) and T (number of triangles used to make a shape). Later on in this investigation T will be substituted for Q (squares) and H (hexagons) used to make a shape. Other letters used in my formulas and equations are X (T, Q or H), and Y (the number of sides a shape has). I have decided not to use S for squares, as it is possible it could be mistaken for 5, when put into a formula. After this, I will try to find a formula that links the number of shapes, P and D that will work with any tessellating shape - my 'universal' formula. I anticipate that for this to work I will have to include that number of sides of the shapes I use in my formula. Method I will first draw out all possible shapes using, for example, 16 triangles, avoiding drawing those shapes with the same properties of T, P and D, as this is pointless (i.e. those arranged in the same way but say, on their side. I will attach these drawings to the front of each section. From this, I will make a list of all possible combinations of P, D and T (or later Q and H).
How far is it true to say that the work of solicitors and barristers has changed so much that it is no longer necessary for there to be two separate professions?
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Maths hidden faces
Maths hidden faces Introduction In this coursework I would be investigating the number of hidden faces in different cubes and cuboids. I would provide predictions to make sure I get the right results. After that I would provide diagrams of the cubes and I would explain how I found it. In each section of a set of cubes I would provide formula's that I would find. I would also give information that the pattern carries on. The reason why I am doing this investigation about cubes is because to find the hidden faces and total faces which would be added near the diagrams. I am going to increase one dimension at a time while holding the other one the same. I will start by holding the width and the height by one while increasing the depth by one. Moving on to deeper investigation I would investigate cubes that have more cubes and rows of cubes which would lead to more accurate results. I would again provide total faces and hidden faces. The reason why I would go into such deeper investigation is because to get more information about the cubes with more of them and check if the pattern carries on. Overall of my coursework I would provide a lot of information about what I have done and how I have done it. The rule that I must beware of is if the hidden faces pattern changes in to a different number that means that something is going wrong. Finally I will find formulas for the nth