mathsI will try to find the correlations between the perimeter (in cm), dots enclosed and the amount of shapes (i.e. triangles etc.) used to make a shape.
. GCSE Maths Coursework - Shapes Investigation Summary 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 correlations 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 attempt to discover a method connecting P (perimeter), D (dots enclosed) and T (number of triangles used to make a shape). shortly 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 likely 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
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.
Hidden Faces Coursework Investigation By Mark Costa Introduction 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. From examining the results of my investigation I will hopefully create a formula for each set of cubes that I exam. The procedure of examining these cubes will be done through drawing 3D pictures of the cubes in their patterns on triangular spotty paper, which I will draw myself. Each set of cubes will contain different patterns that will allow me to exam the cubes in varying scenarios and compare different results and formulas that I will create. Through comparing these scenarios I will then amount to a conclusion that will evaluate what I have covered in my investigation. Background Information I already have obtained some background information from examining the task sheet that is set with the investigation at hand. Each individual cube contains six faces; some may be in view while others will be hidden depending on how the cube is placed. When a cube is placed on a table only five out of six faces are in view, therefore one face is hidden. This simple information could be used to conduct a simple formula: 6(all faces)-(number of viewable faces)=(hidden faces) e.g. 6-5=1 therefore the number of hidden faces would be 1. When five cubes are lined up together in a row, there is a total
Investigating Structures - In this investigation I will be looking at different joints used in building different sized cube shaped structures.
Investigating Structures In this investigation I will be looking at different joints used in building different sized cube shaped structures. I have found that there are four different types of joint: 3-joint 4-joint 5-joint 6-joint The aim of my investigation is to be able to use the length of the cube's edge (n) to find out the number of each different joint in that cube. I have taken n to be the number of rods on a cube's edge. I will start my investigation by drawing simple cube structures on isometric paper. I will draw four structures. A 1 x 1 x 1 cube, a 2 x 2 x 2 cube, a 3 x 3 x 3 cube and a 4 x 4 x 4 cube. These are shown on the isometric paper included. After looking at each I will count the number of each type of joint in each cube, and put my results in a table to make it easier to analyse them. Here is the table: Length of n 3-Joint (c) 4-Joint (e) 5-Joint (y) 6-Joint (X) Total Joints (t) 8 0 0 0 8 2 8 2 6 27 3 8 24 24 8 64 4 8 36 54 27 25 I now have my results, and shall set about finding out their formulae. Firstly I will do the 3-Joint's formula. After looking at the table, I notice that the pattern is that there always 8 3-Joints in a cube. So the formula must be: c = 8 This formula is as above because 3-Joints only occur on the corners of a cube. As there are only eight corners on any sized cube, the answer must be
Past and Present ideas about Schizophrenia
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Wknsss in th Russin govrnmnt nd conomy t th strt of th twntith cntury.
W??kn?ss?s in th? Russi?n gov?rnm?nt ?nd ?conomy ?t th? st?rt of th? tw?nti?th c?ntury m??nt discont?nt gr?du?lly gr?w with most Russi?n p?opl?. Work?rs w?r? p?id v?ry littl? ?nd oft?n h?d to work ov?r 11 hours ? d?y. Only h?lf of th? f?rming l?nd w?s own?d by th?15 million p??s?nt f?mili?s, whil? th? oth?r h?lf w?nt to just 300,000 l?ndlords. In ?ddition, th? Russi?ns lost th? Russo-J?p?n?s? w?r, ?nd this humili?ting d?f??t w?s bl?m?d on th? Ts?r ?nd his gov?rnm?nt. Wh?n prot?stors m?rch?d to th? Ts?r's p?l?c? in St P?t?rsburg in 1905 with ? p?tition for full civil lib?rti?s ?nd b?tt?r rights, soldi?rs fir?d upon th?m ?nd 1000 ?r? thought to h?v? b??n kill?d. "Bloody Sund?y", ?s it w?s c?ll?d, prompt?d ? w?v? of prot?sts ?nd th? ?ss?ssin?tion of th? gov?rnor of Moscow, Duk? S?rg?i. In r?spons? th? Ts?r did introduc? d?mocr?tic r?forms th?t includ?d th? s?tting up of th? Dum?, ? d?puty ?ss?mbly of th? middl? cl?ss; th? form?tion of ? council of minist?rs; ?nd b?tt?r rights for p??s?nts. Th? f?ilur? of th? Ts?r to fulfil ?ll of th? signific?nt d?m?nds m?d? by th? p?opl?, ?nd th? w?y in which h? s??m?d to 'brush th? probl?ms ?sid?' wors?n?d his r?put?tion. H? ?pp??r?d w??k ?nd un?bl? to k??p ?ny promis?s h? m?d?, ?nd wors? still th? d?mocr?tic Dum? h? ?st?blish?d h?ld no ?ff?ctiv? pow?r, ?nd w?s obviously ? ploy to pl??s? th? p?opl? whil? th? Ts?r ignor?d th?m. Th? p?opl?
Maths Cw Borders Investigation Cubes
+4=1*1+2*2 I will construct 2D cross shape but explain them in relation to 3D cross shapes. The Third 3D Cross shape has 13 cubes in its middle layer which is based on its corresponding 2D cross shape. Therefore: 13=4+9 =2*2+3*3 The fourth 3D cross shape has 25 cubes in its middle layer which is based on its corresponding 2D cross shape. 25=16+9 =4*4+3*3 The fifth 3D cross shape has 25 cubes in its middle layer which is based on its corresponding 2D cross shape. 41=16+25 =4*4+5*5 The sixth 3D cross shape has 61 cubes in its middle layer which is based on its corresponding 2D cross shape. 61=25+36 =5*5+6*6 By tabulating all the above result I can derive the general result. Number/level (N) Mn(layer of cubes in the middle layer) =1=1*1=0*0+1*1 2 5=1+4=1*1+2*2 3 3=4+9=2*2+3*3 4 25=9+16=3*3+4*4 5 41=16+25=4*4+5*5 6 61=25+36=5*5+6*6 The first column values of the table were always 1 less than the corresponding cross shape where as the second column values are the cross shape numbers broken up. Therefore the general formula for the Nth cross shape must have (n-1)2+n2 cubes. Mn=(n-1)2+n2 cubes in it Mn=n2-2n+1+n2 Mn=2n2-2n+1, where n cross shape level Mn Number of cubes in the middle layer of nth cross-shape However the result obtained earlier for 2D cross shapes and proved alternatively using triangular numbers but now I have realized that the
I will be investigating different patterns that can be found in cubes that are constructed from smaller 1cm cubes and are painted on the outside.
CUBES I will be investigating different patterns that can be found in cubes that are constructed from smaller 1cm³ cubes and are painted on the outside, when these smaller cubes are taken apart some are only partly painted others none at all. Here is a table showing the number of faces painted. Cube Number Cube length No. Of small cubes No. Of small cubes with 3 painted faces No. Of small cubes with 2 painted faces No. Of small cubes with 1 painted faces No. Of small cubes with 0 painted faces 2 2*2*2 8 8 0 0 0 3 3*3*3 27 8 2 6 4 4*4*4 64 8 24 24 8 Straight away I noticed that the number of cubes with three sides painted is always 8 as seen in the table below and this is true for all cubes except one (see exceptions). Cube Length No. Of small cubes No. Of small cubes with 3 painted faces (Y) 2*2*2 8 8 3*3*3 27 8 4*4*4 64 8 5*5*5 25 8 6*6*6 216 8 There fore the formula for this is simply Y=8 The next table will show the formula to find cubes with two sides painted and I how I found it. Cube Number (X) Cube dimensions No. Of small cubes No. Of small cubes with 2 painted faces (Y) 2 2*2*2 8 0 3 3*3*3 27 2 4 4*4*4 64 24 5 5*5*5 25 36 6 6*6*6 216 48 7 7*7*7 343 60 8 8*8*8 512 72 I first noticed that the number of small cubes (the column in red) was the twelve times table as each number went up in
Persuasive essay
LW 26 Elias, Patrik 82 40 56 96 45 51 8 3 6 1 220 18.2 RW 89 Mogilny, Alexander 75 43 40 83 10 43 12 0 7 0 240 17.9 RW 17 Sykora, Petr 73 35 46 81 36 32 9 2 3 0 249 14.1 C 23 Gomez, Scott 76 14 49 63 1- 46 2 0 4 0 155 9.0 C 25 Arnott, Jason 54 21 34 55 23 75 8 0 3 2 138 15.2 LW 18 Brylin, Sergei 75 23 29 52 25 24 3 1 0 2 130 17.7 D 28 Rafalski, Brian 78 9 43 52 36 26 6 0 1 1 142 6.3 C 16 Holik, Bobby 80 15 35 50 19 97 3 0 3 0 206 7.3 RW 21 McKay, Randy 77 23 20 43 3 50 12 0 5 0 120 19.2 LW 11 Madden, John 80 23 15 38 24 12 0 3 4 1 163 14.1 D 27 Niedermayer, Scott 57 6 29 35 14 22 1 0 5 0 87 6.9 D 4 Stevens, Scott 81 9 22 31 40 71 3 0 2 0 171 5.3 C 12 Nemchinov, Sergei 65 8 22 30 11 16 1 0 2 0 70 11.4 RW 24 Stevenson, Turner 69 8 18 26 11 97 2 0 1 1 92 8.7 D 5 *White, Colin 82 1 19 20 32 155 0 0 1 0 114 0.9 D 6 O'Donnell, Sean ALL 80 4 13 17 0 161 1 0 2 0 67 6.0 MIN 63 4 12 16 2- 128 1 0 2 0 58 6.9 NJ 17 0
look at shapes made up of other shapes
Math's Coursework shapes Summary 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
Investigate the number of hidden faces when cubes are joined in different ways.
Hidden Faces Investigation Investigate the number of hidden faces when cubes are joined in different ways I am going to investigate the number of hidden faces when cubes are joined in different ways. The aim of this task is to find a formula which is common with every cube and hidden face. For this investigation I will need to find the formula, which can determine the outcome for the number of hidden faces on 'n' cubes. I will start this investigation by drawing cubes that join together in rows also those that are joined to form a cuboid. I will draw up a table to show my results, from which I will hopefully be able to find a pattern that will allow me to express a formula that can be used to find the number of hidden faces when cubes are joined in any form i.e. rows and cuboids. Task 1 When placing a single cube on a flat surface only 1 face is hidden out of 6. Fundamentally only 5 faces are visible. Cubes are a three-dimensional shape with six equally-sized square surfaces; if you multiply the number of cubes by 6 (as there are six faces on a cube) 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