Leonardo of Pisa lived in the 13th century in Pisa, Italy. He was
given the nickname Fibonacci because his father’s name was
Bonacci. Among his mathematical explorations is the sequence of
numbers 1, 1, 2, 3, 5, 8, 13, 21, ….
a) Determine the pattern rule for this sequence, and list the next
four terms.
b) Construct rectangles using consecutive terms for the sides.
The first rectangle is 1 by 1, the second is 1 by 2, the third is
2 by 3, and so on. Find the area of each rectangle.
c) Explore the ratios of the sides of the rectangles. Make conjectures
about this ratio.
d) Explore the ratios of the areas of the rectangles. Make conjectures
about this ratio.
+23246 A "recursive" definition is one in which the first term (or terms) are given and the rest of the terms are defined in terms of previous terms.
For the Fibonacci sequence, the first two terms are given, both are "1". After that, each new term is the sum of the previous two terms.
Construct rectangles that are 1x1, 1x2, 2x3, 3x5, etc.
The last two questions are "explore" questions; the intent is for you to learn through the process of exploration, not just repeating the answers of others.
+23246 A "recursive" definition is one in which the first term (or terms) are given and the rest of the terms are defined in terms of previous terms.
For the Fibonacci sequence, the first two terms are given, both are "1". After that, each new term is the sum of the previous two terms.
Construct rectangles that are 1x1, 1x2, 2x3, 3x5, etc.
The last two questions are "explore" questions; the intent is for you to learn through the process of exploration, not just repeating the answers of others.
