Discussing Dеmеntiа.
D?m?nti? D?m?nti? is ? t?rm us?d to d?scrib? th? loss of m?nt?l ?biliti?s. M?mory loss is th? most promin?nt symptom of d?m?nti?, but p?ti?nts c?n ?lso ?xp?ri?nc? imp?ir?d sp??king, und?rst?nding, judgm?nt, ?nd confusion ?bout pl?c? ?nd tim?. D?m?nti? c?n ?ff?ct p?rson?lity, mood, ?nd b?h?vior. Th?s? imp?irm?nts int?rf?r? with ? p?rson's ?bility to p?rform ?v?ryd?y t?sks. Th? most common c?us?s of d?m?nti? ?r? ?lzh?im?r's dis??s? ?nd strok?s ?ff?cting th? br?in. ?lzh?im?r's dis??s? ?ccounts for 50% to 75% of ?ll c?s?s. Strok?, ? kind of v?scul?r dis??s?, is r?sponsibl? for 10% to 20% of c?s?s. L?ss oft?n, d?m?nti? c?n b? c?us?d by oth?r conditions. M?mory loss ?nd confusion c?n b? c?us?d ?lso by ?lcohol, d?pr?ssion, m?dic?tion sid? ?ff?cts, physic?l illn?ss, ?nd oth?r conditions. D?t?rmining if th?s? f?ctors ?r? th? c?us? of m?mory loss or confusion is import?nt b?c?us? tr??tm?nt m?y r?v?rs? or stop th? d?clin? of m?nt?l ?biliti?s. (Goldm?nn, 1999). ?lzh?im?r's dis??s? r?sults wh?n c?rt?in c?lls in th? br?in stop working. It b?gins in th? p?rt of th? br?in controlling m?mory. ?s th? d?m?g? 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.
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.
Math's Painted Cube Investigation Aim: Our aim is to 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. Method: . We drew out all the different sizes of cubes up to 5x5 like the following: x1 cube 2x2 Cube 3x3 Cube 4x4 Cube 5x5 Cube 2. Then counted how many with 1 face painted and imagine the ones that were not shown. 3. The counted how many 2 faces painted and imagine the ones which are not shown. 3.The counted the faces painted and imagined the ones that are not shown. 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 Face Painted 2 Faces Painted 3 Faces Painted x1 0 0 0 0 2x2 0 0 0 8 3x3 6 2 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. We found out the following: 0 Face: 0,0,1,8,27 (Tasneem with the help of the revision guide found out that these numbers were cube numbers). Face:0, 0,6,24,54 (Asma found out these numbers were from the 6 times table). 2 Face: 0,0,12,24,36 (Alliyah and
Lines, regions and cross overs
Aim During this investigation I intend to find the rules and patterns linking lines crossovers and regions. To do this I will produce a series of tables and graphs and look closely to find visible patterns between different parts of my investigation. Prediction I predict that during my investigation I will find patterns that will lead me to be able to make rules about the relationships between lines, cross overs and regions. Plan During my investigation I will investigate the sets of lines with the most amount of cross overs from 1 to 6 lines. I will investigate the amount of cross overs the number of enclosed regions, the number of open regions, difference between the number of cross overs and the amount of closed regions, difference between the number of cross overs and the amount of open regions and the difference between the number of open and closed regions. Then I will produce graphs to enable me to see if I can find any patterns and equations. I will the start working with the fewest number of lines and work up to the maximum and I shall make a table to show my results. Investigation Line For 1 line the maximum you can have is 0 crossovers 0 closed spaces and 2 open Spaces. 2 Lines As you can see the maximum for 2 line is 1 crossovers 0 closed spaces and 4 open spaces. 3 Lines 4 Lines As you can see the maximum for 4 lines is 6 crossovers 3 closed regions
painted sides of a cube
Painted Sides of a Cube By Connor McInnes Here is a 3 x 3 x 3 cube: These 3 cubes all represent 3 x 3 x 3 cubes, the first one has the blocks shaded (pink) that will be painted 3 sides, the second cube has the blocks shaded (blue) that will have 2 sides painted, and the third cube has blocks shaded (green) that will have 1 side painted and all of the remaining cubes will have no sides painted. There is a definite pattern for the cube and the sides painted. After looking at the first 4 cubes, the sides painted look as such: In a 2 x 2 x 2 cube there are: 0 blocks with 0 sides painted. 0 blocks with 1 side painted. 0 blocks with 2 sides painted. 8 blocks with 3 sides painted. In a 3 x 3 x 3 cube there are: blocks with 0 sides painted. 6 blocks with 1 side painted. 2 blocks with 2 sides painted. 8 blocks with 3 sides painted. In a 4 x 4 x 4 cube there are: 8 blocks with 0 sides painted. 24 blocks with 1 side painted. 24 blocks with 2 sides painted. 8 blocks with 3 sides painted. In a 5 x 5 x 5 cube there are: 27 blocks with 0 sides painted. 54 blocks with 1 side painted. 36 blocks with 2 sides painted. 8 blocks with 3 sides painted. I attempted to look for a pattern after constructing the first few cubes and looking at the trends in sides painted for each cube. For 0 sides painted, I found that if n = (the number blocks on one row or column of the
Hidden Faces Investigation
Introduction This piece of coursework investigates 'hidden faces' on objects made up of cubes placed on a flat surface. This coursework focuses on finding a formula for the number of faces of cubes that are hidden from sight. I will use many diagrams and tables to help me arrive at a conclusion to my investigation. Abbreviations In this investigation: Let x be the length, y the height and z the width, of a cuboid made up of single unit cubes like this: x, y and z are collectively z z known as 'the variables'. x Let n be the term number of a cube arrangement. Let h be the number of hidden faces in an arrangement, v the visible faces and T the total number of faces. abc means the number of a with dimensions bc. For example, hxy means the number of hidden faces with dimensions xy. Diff. is short for difference, as in 1st Diff. (First difference, for example) Letters are in bold to distinguish between x (length) and x (multiplication). Contents Title Page Introduction Abbreviations Contents Start of Investigation Proving the general formula for h Testing the formulae for h, v and T in arrangements: With one changing variable With two changing variables With three changing variables Extension More abbreviations Conclusion Start of investigation My investigation begins by looking at an individual cube from 3 angles, to show how many faces there
Maths-hidden faces
Aim: To find a rule in algebra to reveal how many hidden faces there are in a row of cubes, and to use dimensions and the number of shown faces to work out the number of hidden faces in cuboids. Part 1-Investigating the number of hidden faces in rows of cubes Introduction: This part of the investigation is about how many hidden faces there are in a row of cubes. I will be investigating how to work out the number of hidden faces in a row of cubes in algebra, whilst using the number of cubes in a row in the expression, e.g. Number of hidden faces = number of cubes-a specific number. I will also be showing how to work out the number of hidden faces in a row without counting, but instead by using an expression. To prove the expression works I will test and predict the amount of hidden face in a row of cubes by using the rule in algebra. If the rule works then I will be able to explain it and draw diagrams to test the rule in algebra. Results: Number of cubes in a row Number of hidden faces 2 4 3 7 4 0 5 3 6 6 7 9 8 22 Rule: h=3n-2 Key: h=hidden faces, n=number of cubes Explanation of rule: I found my rule by looking at the number of hidden faces on the row of cubes. For each cube in the middle of the row, there are three faces showing and three faces hidden so the first part of my rule was 3n. At the end of each row there are only 2 hidden faces so
I am doing an investigation to look at shapes made up of other shapes (starting with triangles, then going on squares and hexagons
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 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
Skeleton Tower Investigation
Aim A skeleton tower is made up of a stack of cubes with 4 triangular wings on each long face of the cube. Different towers have different numbers of total cubes and the aim of the investigation was to find an nth term and explain the reasons behind it. Towers Tower 1 - 1 cube in centre O in wings Tower 2 - 2 cubes in centre on each wing 4 on wings Tower 3 - 3 cubes in centre 3 on each wing 2 on wings Tower 4 - 4 cubes in centre 6 on each wing 24 on wings Tower No. No. in central stack No. in each wing Total no. in wings Total no. of cubes 0 0 2 2 4 6 3 3 3 2 5 4 4 6 24 28 6 6 5 60 66 2 2 66 264 276 nth Term and Proof For Tower No.6 I counted the cubes in one section (15 for a 6-high tower), multiplied that by 4 since there were four sections (60 for a 6-high tower), and then added the cubes in the middle stack (66 for a 6-high tower). I repeated this procedure for a 12-high tower (66 cubes per section, 264 cubes on wings and 276 total cubes). Using the results I worked out an nth term for the Skeleton Tower: 2n² - n This rule can be proved as two 'arms' unite to form a rectangle with dimensions n by (n-1). There are four arms for the tower so this has to be multiplied by 2 and the center column is added and it has n blocks: The formula 2(n (n-1)) + n is simplified to equal 2n² - n For Tower No.6 = 6 x 5 = 30 30 x 2 = 60
Painted Cube Ivestigation.
Painted Cube Ivestigation This investigation was about investigating what happened when a large cube made up of smaller cubes was put into a pot of paint. First, I labelled the smaller cubes according to their position in the large cube. = Corner Cube = Middle Cube = Core Cube = Central Cube This is my diagram of a 3 x 3 x 3 cube. The Cubes are labelled. If the large cube were covered in paint, not every face on every small cube would be covered. Some cubes, according to position, would have only 1 face painted, some would have 2 faces painted etc. I first investigated a 33 cube. These are my results. Total in Cube (33) Faces Covered (each) Total faces Covered Corner Cubes 8 3 24 Core Cubes 0 0 Middle Cubes 2 2 24 Central Cubes 6 6 Total Faces in Cube Complete Cube 27 62 54 They show: * The total number of cubes of each type in a large cube (33). * 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. Total in Cube (23) Faces Covered (each)
The end of the Jeffersonian Era and its principles
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