Spatial training can also be classified by the type of aid used in the training. Some studies have investigated different means of intervention to develop spatial abilities of students with the aid of: a) tangible models (TMs) (Casey, Pezaris, & Bassi, 2012; Pillay, 1998; Yurt & Sunbul, 2012); b) virtual models (VMs) in interactive computer g... ... middle of paper ... ...), 817– 835. Sorby, S., Casey, B., Veurink, N., & Dulaney, A. (2013). The role of spatial training in improving spatial and calculus performance in engineering students.
[IMAGE] Fig. 1 This is a 3-step stair. The stair total for this stair shape would be: 25 + 26 + 27 + 35 + 36 + 45 = 194 I started simple to form some simple equations to calculate the stair total. Eg 1. For a 3-step stair on a 10×10 grid I came up with the following formula to calculate stair total, based on one of the numbers in the stair shape: [IMAGE] The formula for finding the stair total for a 3-step stair on a 10×10 grid would be: 6x + 44 x being the number in the bottom left of the stair.
Frequently mathematics is used to manipulate complex three-dimensional objects like polygons. They do this by applying textures, lighting and other effects to the polygons and rendering the completed image. Graphical user interfaces are used to create the animation and arrange its choreography. Another technique called constructive solid geometry defines objects by conducting process on regular shapes which gives the advantage and makes it so that animations may be accurately produced at any resolution. Rendering a simple image of a room with flat walls and a pyramid in the middle of the room uses mathematical problems like geometry and ratios.
AIM OF THE EXPLORATION ÿ Explore Integral Calculus usage to find the Volume of the solids ÿ Identify the cross-section of the solid ÿ Suggest an Algorithm for finding an expression for the Volume INTRODUCTION We learnt in the Applications of the Integral calculus to find the area under the curve. This can be divided in following three cases: ÿ Area below any given curve and above the X-axis ÿ Area between the two given curves If definite integration can be used to calculate the area of any figure in XY plane, then there must be some way to calculate the volume of Figures in 3 Dimensional Geometry. can calculus be used for this purpose. Yes definitely, and that is the topic of our exploration. We will try to demonstrate the use of calculus or Definite Integration to find the volume of certain figures having the cross-sections whose area we already know.
In this portfolio task I have investigated the patterns in the intersection of parabolas and various lines. I have formed a conjecture to find the value of D of the parabolas, which are intersected by 2 lines, of varying slopes and shown the proof of its validity. I have used the TI-84 graphic display calculator, the software Geoegebra and Microsoft Excel to do my calculations. I have even investigated the values of D, for polynomials of higher powers and tried to come up with a general solution for all equations. I have been able to do this portfolio from the knowledge learnt from classroom discussions and through various other resources.
Polyhedron Polyhedron is a three dimensional figure made up of sides called faces, each face being a polygon. A polygon is a two dimensional figure made up of line segments called edges that are connected two at a time at their endpoints. In a polyhedron, several polygonal faces meet at a corner (vertex). When all the edges of the polygon are of equal length the polygon is called regular. An equilateral triangle and a square are examples made up of three and four edges respectively.
Visualization also helped me to understand the formula to find the volume of a cylinder. I could see the multiple circles stacked on top of each other to create the 3D shape. Also, I can apply this lesson to real life. Careers like architecture and design jobs depend on these shapes and formulas to create an eye-pleasing design. When building houses you need to know the amount of material you might need for cylindrical pillars to support it which can be found by using the formula, πr²*h, to find the volume of the pillars.
It is an equation a^2+b^2=c^2 but also can be turned into different forms like √(〖(a〗^2+b^2 ))=c or even take a^2 and write as b^2=c^2-a^2. With the algebraic equations the length of each side of an right-angled triangle can easily be calculated. Meanwhile, there are a lot of ways to proof the Pythagorean Theorem, they were all invented by different mathematicians aroung the world at different time, and can proof the theorem using squares, rectangles, trapezium, circles and much more shapes. There are over three hundred proofs currently. With all these different proofs we can believe that the theorem is most likely correct.
Where: fct is the splitting tensile strength in MPa; fcy is the cylinder compressive strength in MPa; fcu is the cube compressive strength in MPa. Figure (2.26): Splitting tensile strength vs. compressive strength. (Shafigh, Jumaat, Ahmud, Anjang and Hamid, 2012) 220.127.116.11.3. The ratio between the flexural strength and splitting strength: 18.104.22.168.3.1. For normal concrete: An attempt was made to report the comparative analysis of the modulus of rupture and the splitting tensile strength of normal concrete by (Akinkurolere, 2010).
In figure (2.26), eight equations proposed by different researchers have been plotted for lightweight concrete, as shown in table (2.12). The experimental splitting tensile strength values are calculated as follows: Eq. (2.23), (2.24), (2.25) (2.26) for cube specimens and (2.27), (2.28), (2.29), (2.30) for cylinder specimens. The splitting tensile strength of lightweight concrete for Eq. (2.23) ranged from 2.8 – 3.5 MPa, as shown in figure (2.23).