GCSE: Hidden Faces and Cubes
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Virtul Orgniztions
Inform?tion syst?ms m?k? virtu?l org?niz?tions mor? succ?ssful, b?c?us? th? communic?tion ?nd coll?bor?tion ?mong disp?rs?d busin?ss p?rtn?rs is k?y to m?king it h?pp?n. Busin?ss p?rtn?rs c?n us? diff?r?nt inform?tion syst?ms on diff?r?nt t?chnologic?l pl?tforms. In th? p?p?r w? will discuss th? possibiliti?s for inform?tion?l support of th? coop?r?tion b?tw??n p?rtn?rs within virtu?l n?tworks with focus on ?nt?rpris? r?sourc? pl?nning solutions, which b?c?m? mor? ?nd mor? import?nt. Virtu?l Org?niz?tions In busin?ss ? n?w p?r?digm, in which knowl?dg? ?nd s?rvic? b?s?d syst?ms ?r?
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Maths Investigation Painted Cubes
As I built and drew more and more cubes, it became much more apparent, which reinforced my previous hypothesis. Results Table Cube Size n x n x n No. of cubes with 3 faces painted No. of cubes with 2 faces painted No. of cubes with 1 face painted No. of cubes with 0 faces painted Total No. of cubes 2 x 2 x 2 8 0 0 0 8 3 x 3 x 3 8 12 6 1 27 4 x 4 x 4 8 24 24 8 64 5 x 5 x 5 8 36 54 27 125
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Discussing Dеmеntiа.
progr?ss?s, p?opl? with ?lzh?im?r's dis??s? ?lw?ys g?t wors?. For most p?opl?, this is ? slow proc?ss, but for som?, it is r?pid. P?opl? with ?lzh?im?r's dis??s? liv? ?n ?v?r?g? of 8 to 10 y??rs ?ft?r th? di?gnosis. Som? liv? 20 or mor? y??rs. Th? c?us? of ?lzh?im?r's dis??s? is unknown. Old?r ?g? ?nd ? f?mily history of d?m?nti? incr??s? ? p?rson's ch?nc? of g?tting d?m?nti?. Whil? th?r? is no cur? for ?lzh?im?r's dis??s?, th?r? ?r? m?dic?tions to slow progr?ssion of th?
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Wknsss in th Russin govrnmnt nd conomy t th strt of th twntith cntury.
Ts?r ignor?d th?m. Th? p?opl? unwilling to l?t th? Ts?r continu? his rul?, th?t w?s n??ring dict?torship, form?d v?rious opposition p?rti?s in Russi?. Th? m?in group w?s th? Soci?list R?volution?ri?s, ?nd th?y g?in?d much support from th? p??s?nts who sought ? r?dic?l solution in Russi?. ?noth?r w?s th? Russi?n Soci?l D?mocr?tic p?rty, found?d in 1898, it ?pp??l?d to m?ny town work?rs but th?n split in 1903 to th? Bolsh?viks ?nd th? M?nsh?viks. Both groups follow?d M?rxist id?ology but h?d diff?r?nt ?ppro?ch?s to ch?ll?nging th?
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Investigate the number of ways there are of arranging cubes on different sized grids.
I do not think I have to go further with this investigation. I can see that there are 5 arrangements for placing 4 cubes on 5 cubes on a 2 x 3 grid. If I multiply them together: 5 x 6 = 30, it should equal the amount of arrangements. This has proved that my prediction will be correct. Now I can move on to the next investigation. Part 3: For the third part, I will be trying to find out how many ways there are of placing 6 cubes on top of 7 cubes on a 2 x 4 grid.
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Hidden Faces
48 26 22 The graph above show the number of hidden faces, the number of faces which can be seen and the total number of faces. Nth term 1 2 3 4 5 6 7 8 Total faces 6 12 18 24 30 36 42 48 difference + 6 + 6 + 6 + 6 + 6 + 6 + 6 The table above shows the total number of faces on an 'n' number of cubes. As we increase the number of cubes being added on the number of faces increases by 6.
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Hidden Faces.
17 20 23 26 Difference +3 +3 +3 +3 +3 +3 +3 +3 Nth term 1 2 3 4 5 6 7 8 Total No. of Faces 6 12 18 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.
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Mathematics GCSE  Hidden Faces.
Row 2 Row 3 Row 1 Instead of trying to find the number of hidden faces I looked at the visible faces and I took that away from the total amount of faces. You can see 3 rows first, so the number of visible faces for those three rows is 3(n then there is one visible side on each side, so I added 2, so the number of shown faces is 3n+2. In order to work out the number of hidden faces I found the total number of faces and took away the number of visible faces, which equals to 6n(3n+2), which is equal to 3n2.
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Find 4 formulae that can work out the number of cubes in a cube that has been painted on the outside with 0 faces painted, 1 face painted, 2 faces painted and 3 faces painted in any sized cubes.
4. Next we recorded our results in a results table. 4. We then found formulae for them. Results: All results were recorded in a table, so if a pattern were to occur, it would be easier to spot. Size of cube 0 Faces Painted 1 Face Painted 2 Faces Painted 3 Faces Painted 1x1 0 0 0 0 2x2 0 0 0 8 3x3 1 6 12 8 4x4 8 24 24 8 5x5 27 54 36 8 Next we tried to see if there was a pattern like square numbers, cube numbers, triangular numbers, odd numbers or even numbers.
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Investigate different sized cubes, made up of single unit rods and justify formulae for the number of rods and joints in the cubes.
1046 The problem is to find formulae that represent the number of rods, 3 joints, 4 joints, 5 joints and 6 joints in an n x n x n cube. And then repeat for a cubiod Cubes (Sheet 1) I started the Investigation by drawing a cube shape. I thought 5 different sized cubes would be enough to work out formula and trends that may come up. I increased the cubes 1cm2 each time, starting with 1 x 1 x 1.
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With Close Reference to The Wasteland and the Great Gatsby Compare and Contrast how and why Eliot and Fitzgerald use their Chosen Genres to Explore Sexual and Emotional Relationships.
x"HPRNTWNPRL"`FRAMFRAM ��f deft conWith Close Reference to The Wasteland and the Great Gatsby Compare and Contrast how and why Eliot and Fitzgerald use their Chosen Genres to Explore Sexual and Emotional Relationships The Great Gatsby by Scott Fitzgerald and The Waste Land by T.S. Eliot represent two pieces of significant post war social commentary, being published in 1925 and 1922 respectively. Eliot adopting modernism and Fitzgerald; realism, are both used to reflect on the changing 1920s social climate. In each work, the issue of sexual and emotional relationships is explored to reveal the corruption of the society being discussed .
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Investigation into the progression of patterns in 3d shapes.
In pattern 1, layer A = 0 therefore it is a step behind. The progression of layer B is again the same however the formula is different. In pattern 2 layer B = 0, therefore it is two steps behind. The results of my investigation can be shown as follows: C B A Centre layer A B C Nth Term 1 n = 1 1 5 1 n = 2 1 5 13 5 1 n = 3 1 5 13 25 13 5 1 n = 4 5 13 25 41 25 13 5 n = 5 My table
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Painted Cube Ivestigation.
* The number of faces, of each cube type, covered. * The total number of faces covered for each cube type. * And the total number of faces in the large cube (33) Then I realised that I had started at 33 and had not done 23 or 13. The interesting thing about 13 is that it is made up of only 1 cube. This cube is as much a corner cube as it is a core cube. I think that 13 Is no help to my investigation because the results in the table are so uniform.
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Investigate the number of hidden faces when cubes are joined in different ways.
the outcome you will get is the total number of faces. Example: How many faces are there in total when 3 cubes are joined together? By using the above theory: 'multiply the number of cubes by 6', thus 3 x 6 = 18 There are 2 ways to find the total number of faces on cube(s), one being the above example and the second being, by multiplying six by the length, width and height of the cube to give me the same result.
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Hidden Faces.
And if a cube is put is put next to another there are always two hidden faces between them. Number Of Cubes Number Of Hidden Faces 1 4 7 10 13 16 19 What This Shows: My results show a pattern occurring. For every cube that is added the number of hidden faces grows by three each time. I my table the number of hidden faces are lade out in a sequence. This will help me to find a formula so I can work out the number of hidden faces without having to count them each time. To show how I know the numbers are in sequence I will use my knowledge of methods of difference.
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Face Recognition.
Bruce and Young (1986) proposed a top  down approach to face recognition in which they argued that recognising a face is a highly complex process involving stored knowledge of semantic and emotional information and is therefore much more than adding together the sum total of a face's features. According to the Holistic approach a face is recognised as a whole, analysing not just the separate features but also the configuration of the face, the relationship between the individual features, feelings aroused by the face and semantic information about the face. Such an approach is sometimes referred to as a template model (Ellis 1975)
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Investigating 'Painted cubes'.
I noticed that the columns for 3 faces had a pattern except 1 x 1 x 1.
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Find out how many different combinations 5 cubes can make on top of a 2 by 3 base.
Fig 3: The 6 combinations Square with cube Empty space This diagram of the 6 combinations shows the symmetry of the combinations when shown together. 2) On the second layer there is one less place to put a space so one less combination can be made and as there are five places to put a space on this layer there are 5 different combinations that the second layer can make. Once again like in question one there will be a space on this layer that will move around to create different combinations.
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Hidden faces investigation.
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.
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Cubes and Cuboids Investigation.
Also if you look at the diagram above you can see that all the cubes with two painted (brown) are one in from either side and so the formula must have X2 in it which is the cube length minus 2. Therefore the formula is Y=12(X2). 'fontsize:14.0pt; '>Now I have found out the formula for cubes with 3 or 2 faces painted. 'fontsize:14.0pt; '>Here is the table showing the cubes with one painted face: cube length (X) No. of cubes with 1 painted face (Y)
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Investigate the number of hidden faces when cubes are joined indifferent ways.
Then try different formulas and see if it fits with the set of results. Part one: Number Of Rows 1 When a single cube is placed on a flat surface only 1 face is hidden out of 6 When two cubes are joined together and placed on a flat surface there are 4 hidden Faces out of a possible 12 When three cubes are joined there are 7 hidden faces There are 10 hidden faces There are 13 hidden faces There are 16 hidden faces Results Differences: There is a difference of +3 every time There are 4 hidden faces
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The aim of my investigation is based on the number of hidden faces and faces in view of cubes that are placed on a table.
Thirteen of these faces are hidden; the number of faces hidden confirms my first formula: 3017=13. Through confirming my first formula I will now be able to predict further sets of cubes such as a row of eight cubes placed on a table. So... 6(number of faces per cube) x8 (number of cubes)=48(number of faces all together) 27 faces in view Therefore: 48(number of faces all together)27(number of faces in view)=21(number of hidden faces) I will now conduct an experiment with Lego cubes that connect together, thus simulating the cubes on the table. I will simulate the set of eight cubes on a row and see if the results match that of my formula.
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The aim of this coursework is to find a global formula for the total number of hidden faces for any number of cubes in rows.
For me to find out the general formula I will have to do one more table for the number of hidden faces. Number Of Cubes. 1 2 3 4 5 6 7 8 Hidden Faces. 1 4 7 10 13 16 19 22 1st Difference + 3 + 3 + 3 + 3 In the table above there is only one line of difference, which tells me that it is a linear equation The general form of a linear equation is: y=mx+c Therefore the linear rule is in the form of: tn=an+c tn=3n+c In the above equation, the total number of hidden faces is tn and n is the number of cubes.
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I am going to investigate different sized cubes, made up of single unit rods and justify formulae for the number of rods and joints in the cubes.
Without using diagonals, this is the most amount of rods to join together. The problem is to find formulae that represent the number of rods, 3 joints, 4 joints, 5 joints and 6 joints in an nxnxn cube. And then repeat the investigation but for an xxyxz cuboid. Stradegy To carry out this investigation, I will need to spot patterns that may emerge as the cube/cuboid gets bigger. Using visual images will aid me greatly in this respect and so I will present the cubes that I am investigating on geometric or spotty paper.
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