Liber Abaci Collection

In 1202, Leonardo of Pisa, known as Fibonacci, formally introduced the Hindu-Arabic numerals to the Western world. His book Liber Abaci (the Book of Calculation) advocated for the simplicity and efficiency of the system, in stark contrast with the one relying on Roman numerals, and provided methods of calculations to be used by mathematicians and merchants.

Leonardo of Pisa

A portrait of Cheng Dawei

The geometry problems below are  adapted from problems appearing in chapter 15 of Liber Abaci. In the original text, the author provides a thorough solution to each question, sometimes including also a solution to a second version of the problem, which is also reflected below.

Source: L.E. Sigler (2002) - Fibonacci's Liber Abaci : Translation into Modern English of Leonardo Pisano's Book of Calculation.

Liber Abaci Collection

"On a certain ground are standing two poles that are only 12 passibus apart, and the lesser pole is in height 35 passibus, and the greater 40 passibus; it is sought, if the greater pole will lean on the lesser, then in what part of it will it touch."

[Adapted from L.E. Sigler's  translation of Liber Abaci (p. 543)]

A Problem on Two Poles I

Where do the poles touch when the 40-foot pole is leaning against the 35-foot pole.

A Problem on Two Poles II

Where do the poles touch when the 35-foot pole is leaning against the 45-foot pole.

2 Birds Flying from 2 Towers

A 40-foot pole is leaning against a 35-foot pole. Where do the poles touch? The distance between them is 12 feet.

2 Birds Flying from 2 Towers

What is the height of each polygon?

"How Deep is the Pond?" problem as illustrated in Suanfa Tong Zong