At stage 1 each side of the equilateral triangle is replaced by the zigzag line as shown on the page 7 against the label stage 1 with each segment of the zigzag line being of length 1/3. At this stage for each side of the equilateral triangle in the stage 0 there are 4 sides and thus the total number of sides is 4*3=12 and perimeter is calculated by the number of sides times the length of a side in this stage i.e…
1/3*1/3=1/9. Thus the number of sides is increased by 4 times i.e. 4*12=48. Length of the side is decreased by 3 times. The perimeter is calculated directly as number of sides in this stage multiplied by the length of the side in the same stage i.e.48*1/9. Now each side in the previous stage gives rise to one equilateral triangle in this stage with side 1/3 of the side in the previous stage i.e.1/9. Therefore the number of new triangles added in this stage is equal to the number of sides in the previous stage i.e. 12. Therefore the area in this stage is calculated as the area in the previous stage plus the sum of the areas of the newly developed triangles.
In the above graph the stage number is taken on x-axis and the no. of sides are taken on y-axis. It shows that the no. of sides increases with the stage number. As n-> Nn ->, since in the limiting situation the fractal does not have an edge but is bound by a smooth curve.
In general for any n>0 ,
Nn = 3*4n = N0*4n
the graph shows that the length of side decreases with the stage no. and finally converges to 0. i.e. the limiting fractal will not have any edges but will be bound by a smooth curve.
In = 1/3n
The graph shows that the perimeter increases with the stage no. but it cannot tend to infinity as the area is bounded by 0.7 as can be seen from the subsequent graph.
Pn = Nn*In
Q7 part 2) The graph shows that area increases with stage number but it does not exceed 0.7 as the curve is tangential to the line y=0.7. in fact as n-> the area tends to 0.7.
An = A0(1+3(k=0 to k=n-1, j=1 to j=n-1[4k*1/32*j]))
= A0(1 + 3(40*1/32 + 41*1/34 + 42*1/36 +..+ ...
Cite this document
(“Maths investigation Essay Example | Topics and Well Written Essays - 750 words”, n.d.)
Retrieved from https://studentshare.net/science/281666-maths-investigation
(Maths Investigation Essay Example | Topics and Well Written Essays - 750 Words)
“Maths Investigation Essay Example | Topics and Well Written Essays - 750 Words”, n.d. https://studentshare.net/science/281666-maths-investigation.
Problem A: Two examples of student’s misconception that could cause this error can be firstly the concept of multiplication of signed numbers is not clear among the students. They might have a misconception that when numbers of opposite signs are multiplied with each other the sign of the greater number which is multiplied will be there on the product or will affect the sign of the product.
It enables us to learn new skills and to form habits. Without the ability to access past experiences or information, we would be unable to comprehend language, recognize our friends and family members, find our way home, or even tie a shoe. Life would be a series of disconnected experiences, each one new and unfamiliar.
Talking also helps the children to think aloud and to think logically, and to discuss, to reason and to present the information and their thoughts effectively and with clarity. Talking involves two essential elements - the 'process' of using the spoken language and the 'content' of the language used.
ar grids whose columns exceed the rows by only one unit in the grid, however we will investigate the relationship that exist in the rectangles whose rows exceed the columns by one unit, therefore we will consider a 3X2, 4X3 and 5X4.
From the above calculations we can conclude
A logistic model takes a similar form to the geometric, but the growth factor depends on the size of the population and is variable. The growth factor is often estimated as a linear function by taking estimates of the projected initial growth rate and the eventual
erested in studying mechanical engineering technology programme because it is a matter-of-fact, modern short course that enables me to develop strong industrial, evaluating, and setback unravelling skills, which are compulsory in the competitive field of mechanical engineering.