Lesson 21 of 1524
Math and art
The Fibonacci sequence adds the two previous terms, and a tessellation covers the plane with no gaps.
Practice this chapterThe Fibonacci sequence used here begins 1, 1, 2, 3, 5, 8, 13. Each new term is the sum of the two before it. The ratio of one term to the previous term approaches the golden ratio, about 1.618.
Reflection, rotation, and translation are three different symmetries. A tessellation covers the plane without gaps and without overlaps.
The next Fibonacci term
next = previous + the one before that
You only need the last two terms.
Worked example
The sequence reaches 8, 13. What comes next?
- 1A Fibonacci term is the sum of the two terms before it, not their product and not one more than the last term.
- 2The two terms you have are 8 and 13.
- 3Add them: 8 + 13 = 21. That is the next term.
- 4The term after that would be 13 + 21 = 34. The question asks only for the next one, which is 21.
Result: 21
Why. 21 is next because it is 8 + 13, the sum of the two previous terms. That is the whole rule. Nothing else in the sequence is needed once those two terms are known.
The golden ratio is about 1.618, not exactly 1.6, and it is the limit of the ratios, not one of the early Fibonacci numbers.
Practice margin
This chapter
A fresh set from this chapter only. Choose 10 or 20. Multiple choice and fill-in, with no repeat inside the set.