(a)
To explain:
The calculations in the given chart.
Step | Number of Triangles | Length of Each Side | Perimeter of One Triangle | Total Perimeter of All Triangles |
1 | ||||
2 | ||||
3 | ||||
4 | ||||
5 | ||||
6 |
(b)
To find:
The remaining values in the given table.
(c)
The factor by which the number of triangles increases and explain the answer.
(d)
The factor by which the length of each side decreases and explain the answer.
(e)
The factor by which the perimeter of one triangle changes, explain the answer and determine if the perimeter of one triangle is increasing or decreasing.
(f)
The factor by which the total perimeter of all new triangles changes, explain the answer and determine if the total perimeter of all new triangles is increasing or decreasing.
(g)
To find:
The formula for the total perimeter of all new triangles at step
(h)
The perimeter of the Sierpinski gasket.
Trending nowThis is a popular solution!
Chapter 8 Solutions
Mathematics: A Practical Odyssey
- The Unified Thread may have either a flat or rounded crest or root (Figure 4-6). If the sides of the Unified Thread are extended, a sharp V-thread is formed (Figure 4-7). In Figure 4-7, H is the height of a sharp V-thread. The pitch, P, is the distance between two adjacent threads. Find dimensions A, B, and C as indicated. a. H=716A=_,B=_ b. H=38A=_,B=_ c. H=1516A=_,B=_ d. H=2132A=_,B=_ e. H=34A=_,B=_ f. P=14C=_ g. P=332C=_ h. P=120C=_ i. P=128C=_ j. P=316C=_arrow_forwardRefer to the shaft shown in Figure 6-4. Determine the missing dimensions in the table using the dimensions given. All dimensions are in inches.arrow_forwardThis casting in Figure 5-4 shows seven tapped holes, A-G. The number of threads is determined by dividing the depth of the thread by the thread pitch. Find the number of threads in each of the tapped holes. All dimensions are in inches. A=_B=_C=_D=_E=_F=_G=_arrow_forward
- Determine the length of the template in Figure 4-3. All dimensions are in inches.arrow_forwardDetermine dimensions A, B, C, D, E, and F of the drill jig in Figure 35. All dimensions are in inches. A = ______. B = ______. C = ______. D = ______. E = ______. F = ______.arrow_forwardDetermine dimensions A, B, C, D, E, F, and G of the tapered pin in Figure 3-6. All dimensions are in inches. A = ______. B = ______. C = ______. D = ______. E = ______. F = ______. G = ______.arrow_forward
- A diagonal of a cube joins two vertices so that the remaining points of the diagonal lie in the interior of the cube. Show the diagonal of the cube having edges of length e is e3 units long.arrow_forwardDetermine dimensions A, B, C, D, and E of the template shown in Figure 4-4. All dimensions are in inches. A = . B = . C = . D = . E = .arrow_forwardDetermine dimensions A, B, C, D, E, F, and G of the plate in Figure 2-5. Reduce to lowest terms where necessary. All dimensions are in inches. A = ______. B = ______. C = ______. D = ______. E = ______. F = ______. G = ______.arrow_forward
- Plans call for triangle BCDto be sheared off a corner of a rectangle as shown in the figure. A decision is made to move one vertex of the triangle 1.5 in. from B to B' and the other vertex from D to D'. How much larger is the area of AB' D' than ABDEF ?arrow_forwardIn Exercises 44 and 45, use the formula from Exercise 43. Similar triangles were used to find h and H. A container of yogurt has the shape of a frustum of a cone. With the lower base having diameter length 6 cm and the upper base having diameter length 8 cm, the volume of such a container 7.5 cm tall can be determined by using H=30 cm and h=22.5 cm. Find its volume. A frustum of a cone is the portion of the cone bounded between the circular base and a plane parallel to the base. With dimensions are indicated, show that the volume of the frustum of the cone is V=13R2H13rh2arrow_forward
- Mathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning
- Elementary AlgebraAlgebraISBN:9780998625713Author:Lynn Marecek, MaryAnne Anthony-SmithPublisher:OpenStax - Rice UniversityElementary Geometry For College Students, 7eGeometryISBN:9781337614085Author:Alexander, Daniel C.; Koeberlein, Geralyn M.Publisher:Cengage,Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage