Sierpinski's triangle. A geometric figure known as Sierpinski’s triangle is constructed by starting with an equilateral triangle as in the figure. Assume that each side of the triangle has length 1. Inside the original triangle, draw a second triangle by connecting the midpoints of the sides of the original triangle. This divides the original triangle into four identical equilateral
- When a process is repeated over and over, each repetition is called an iteration. How many triangles will the fourth iteration have?
- How many triangles will the fifth iteration have?
- Find a formula for the number of triangles in the nth iteration. Use mathematical induction to prove that this formula is correct.
Want to see the full answer?
Check out a sample textbook solutionChapter 11 Solutions
College Algebra and Trigonometry (4th Edition)
- Algebra: Structure And Method, Book 1AlgebraISBN:9780395977224Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. ColePublisher:McDougal LittellHolt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGALElementary Geometry For College Students, 7eGeometryISBN:9781337614085Author:Alexander, Daniel C.; Koeberlein, Geralyn M.Publisher:Cengage,
- Mathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,Trigonometry (MindTap Course List)TrigonometryISBN:9781305652224Author:Charles P. McKeague, Mark D. TurnerPublisher:Cengage LearningTrigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage Learning