by G. S. Carr called Synopsis of Elementary Results in Pure Mathematics. Ramanujan used this to teach himself mathematics. The book contained theorems, formulas and short proofs. It also contained an index to papers on pure mathematics. By 1904 Ramanujan had begun to undertake deep research. He investigated the series (1/n) and calculated Euler's constant to 15 decimal places. He began to study the numbers, which is entirely his own independent discovery. Ramanujan, on the strength of his good schoolwork
dimension. Instructional programs from prekindergarten through grade twelve should enable students to understand measurable attributes of objects and the units, systems, and processes of measurement. Also, apply the appropriate techniques, tools, and formulas to determine measurements (NCTM, 171). This paper will describe how those ideas are developed in grades three through five. The first and most basic standard for measurement at this level is being able to understand measurement attributes that we
square and a 5 by 5 square. After doing this, I will try to find a formula that can find the difference in any sized square. I will then decrease the size of the grid so that it becomes 9 by 9 and will then do exactly the same method as I did before and then I will do this again but with a 5 by 5 grid. I will then work out formulas for both of these grids, to find the difference. I will then use algebra to prove that my formulas are able to work out the correct difference. To investigate further
dry, the large cube was cut up into the smaller cubes, all 8000 of them. From there, I had to answer the question, 'How many of the small cubes will have no red faces, one red face, two red faces, and three faces?' From this, I hope to find a formula to work out the number of different faces on a cube sized 'n x n x n'. Solving the Problem ------------------- To solve this problem, I built different sized cubes (2 x 2 x 2, 3 x 3 x 3, 4 x 4 x 4, 5 x 5 x 5, 6 x 6 x 6, 7 x 7 x 7, 8 x 8
measurements, are shown how to administer a test to students, adults, etc… Then shown to calculate the different results and the different formulas we use and what the formulas mean. We also use the calculator, especially a calculator with graphing functions, to make graphs and to see what the math formula actually did. We can see what it measures and actually what the formula means. In another class called Senior research, we are using the ANOVA (Analysis of Variance) which is a data analysis tool that
foundation of Brahmanic Hinduism. The main body of Rigveda's text contains mostly hymns dedicated to the ancient Hindu gods. The second text of Vedas is called the Yajurveda. It was written in 1200 BC. The main themes of Yajurveda are the sacred formulas recited by Brahmin priests during the performance of sacrifices. The third book of Vedas, Samveda (1100 BC), was also known as the Veda of chants. In its essence Samveda was an anthology of Rigveda writings. The last Veda is the Arthaveda (1200 BC)
Elasticity of Demand for Lottery Tickets Elasticity is the responsiveness of demand or supply to the changes in prices or income. There are various formulas and guidelines to follow when trying to calculate these responses. For instance, when the percentage of change of the quantity demanded is greater then the percentage change in price, the demand is known to be price elastic. On the other hand, if the percentage change in demand is less than then the percentage change in price; Like that
The Formula of Succinic Acid Succinic acid is a diprotic, which means it donates two protons per molecule. Succinic acid can be completely neutralised by sodium hydroxide. The indicator most suitable for this experiment is phenolphthalein, it is colourless in acids and pink in alkalises. The half way stage is about pH 9.3, this is when it will either change from colourless to a very pale pink or from pink to colourless. To determine the relative formula mass of succinic acid I am going to
put letters into a formula. This is how it would look: (P+10)(P+1)- P (P+11) = 10 When we multiply out this formula it looks like this: P²+11P+10 -P² - 11P = 10 As it shows the result is 10 once again P²+11P+10 -P² - 11P = 10 Testing the Formula Now we can put the formula to the test by using it with numbers: (23x32)- (22x33) =10 [IMAGE][IMAGE] = As we can see the formula has proven to work well and the result is once again 10 as the formula suggests. Now that
of the 27; have no labels, 1 label, 2 labels and 3 labels. Once I have done this I will the do the same for a 4x4x4 cube, 5x5x5 cube and finally a 6x6x6 cube and see if I can find a pattern. When I have found a pattern I will try to work out a formula and test if it works. 4x4x4 [IMAGE] [IMAGE][IMAGE][IMAGE][IMAGE] [IMAGE][IMAGE][IMAGE][IMAGE][IMAGE][IMAGE][IMAGE][IMAGE] 3x3x3 [IMAGE][IMAGE][IMAGE][IMAGE] [IMAGE][IMAGE][IMAGE][IMAGE][IMAGE][IMAGE][IMAGE] Key [IMAGE][IMAG
It seems like everywhere you look there is some new diet plan making miraculous promises of weight loss through pills, plans, and formulas. The zone diet is no exception. The zone diet was developed by Dr. Barry Sears in his book," Enter the Zone" which was on the bestseller lists for weeks. The zone promises high energy, weight loss, and no hunger to those willing to follow the simple set of zone rules. It sounds great you say, but does it really work? What is the Zone? The "zone" was first
the reader look to the bottom of the page and thus think about what he is proposing. His combination of elevated diction along with deductive reasoning can sometimes lose the reader, but just as fast as the reader is lost Nietzsche offers forth a formula which helps the reader follow his thinking. Nietzsche believes that a person’s "virtue is the consequence of happiness," or that a person’s emotions are the product of their beliefs. Nietzsche’s uses consequence to mean something more like cause than
place a larger disc on top of a smaller disc. You must also complete this task in the smallest amount of moves possible. Our ultimate task was to complete the game with 4 discs and then 5 discs using the smallest amount of moves, then to find a formula to find the smallest amount of moves for any number of discs. Simple cases: ============= 4 discs ======= After having tried to solve the puzzle with 4 discs I found that the smallest amount of moves possible was 15. (See fig
arrangement is: LCUY This combination consists of all the letters being different. I will also try and find a formula for this arrangement, and number of letters. Once I have discovered these formulae I am going to investigate, other combinations of letters and different amounts of letters. I will then try to discover a link between the formulae to enable me to find a formula for the general case. ARRANGEMENTS IN THE NAME LUCY LUCY UCYL CYUL YCUL LUYC UCYL CYUL YCUL LCUY ULCY
Growing Squares I have decided to find a formula to find the nth term. To help me find the nth term I shall compose a table including all the results I know. Pattern Number Number of Squares 1st Difference 2nd Difference 1 1 4 4 2 5 8 3 13 4 12 4 25 The 2nd difference is constant; therefore the equations will be quadratic. The general formula for a quadratic equation is an2 + bn +c. The coefficient of n2 is half that of the second
a fixed refrain in alternation with a lead singer who has more freedom to improvise". This is an important part of rap music. Cheryl Keyes explains, "Audience response helps to prolong performance and helps the rapper to spontaneously execute rap formulas. The more verbal and kinesic the response from the audience, the longer the rapper raps"(146). Another technique used in rap music is the talking over pre recorded tracks. This is defined by Grolier also in the definition of rap music, "a combination
(highlighted above) I will develop a formula to work out the total value of the numbers added up. The boot will consist of three numbers up and two across. My formula must show how to find out the added value of the boot if placed anywhere within the grid. Grid 5x5 ======== 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 I found that in grid 5x5 that the formula for the added value of the boot
Tangents and Normals of Curves If you differentiate the equation of a curve, you will get a formula for the gradient of the curve. Before you learnt calculus, you would have found the gradient of a curve by drawing a tangent to the curve and measuring the gradient of this. This is because the gradient of a curve at a point is equal to the gradient of the tangent at that point. Example: Find the equation of the tangent to the curve y = x³ at the point (2, 8). dy = 3x² dx Gradient
number of Triminoe cards in a set and the largest number used in a set. 2. Investigate the relationship between the sum of all numbers on a set of Triminoe cards and the largest number used on the cards. PLANNING These are some of the formulas I will be using in order to complete the tasks: f (n) =an+b (Linear equation) f (n) =an2+bn+c (Quadratic equation) f (n) =an3+bn2+cn+d (Cubic equation) f (n) =an4+bn3+cn2+dn+e (Quartic equation) METHOD 1. First I am going to the
because the integers less than 12 which have no factors in common with it except for 1 are 1,5,7,11 i.e. there is 4 of them. I started to investigate the phi function of numbers from 2 to 24 so I could find patterns, which I can use to create a formula for the[IMAGE](n) term [IMAGE](n) Shared factors Not sharing factors [IMAGE] (2) - 1 [IMAGE] (2) = 1 [IMAGE](3) 1,2 [IMAGE](3) = 2 [IMAGE](4) 2 1,3 [IMAGE](4) = 2 [IMAGE](5) 1,2,3,4 [IMAGE](5) =