A news item that caught the first author’s attention last year was one that appeared on Mail Online (http://www.dailymail.co.uk/news/article-5062993/Poland-tells-couples-multiply-like-rabbits.html), in which the Polish government was reported to encourage its citi­zens to “multiply like rabbits”. The propensity of rabbits to breed profusely may have instigated the problem posed by Leonardo of Pisa (c.1175-1250), better known as Fibonacci, in his book Liber Abaci, published around 1200: 

A certain man put a pair of rabbits in a place surrounded on all sides by a wall. How many pairs of rabbits can be produced from that pair in a year if it is supposed that every month each pair begets a new pair which, from the second month on, becomes productive?

Fibonacci’s name is mainly associated with the sequence of numbers arising from this puzzle, namely 1, 1, 2, 3, 5, 8, …, each number, or term, in the sequence being the sum of the previous two terms. This sequence of numbers did not generate any particular interest until the French mathematician Edouard Lucas (1842-1891) developed a sequence based on that of Fibonacci. Since then, interest has not waned.

Fibonacci’s contribution to mathematics goes beyond this mere sequence of numbers. In­deed, he was one of the pioneers to introduce Hindu-Arabic numbers to Europe. Fibonacci tra­velled widely to countries such as Syria and Egypt, where he learnt the ways used in these countries to calculate mathematics. Back in Europe he wrote about the methods he had learnt in his famous book, copies of which still survive.

What is perhaps so fascinating about the sequence derived from the rabbit problem are the many interesting mathematical properties inherent in the famous se­quence of numbers, which, Fibo­nacci himself was probably not aware of. For example, any two consecutive numbers in the sequence are relatively prime, that is, their greatest common divisor is 1. Perhaps even more fascinating is the apparent ubiquity of the numbers in nature. For example, the number of spirals in successive directions of a pinecone, the leaf arrangement in plants and the pattern of the florets of a flower tend to consist of numbers from the Fibonacci sequence. Maybe, as Galileo Galilei pointed out, the laws of nature are indeed written in the language of mathematics.

Did you know?

The Malta Mathematics Olympiad’s origins, history

• The first edition of the Malta Mathematics Olympiad was held in 2000, which was desig­nated as the World Mathematical Year by the International Mathematical Union.

• The aim of the Malta Mathematics Olympiad is to foster problem-solving skills in young students in an atmosphere of healthy competition as well as to promote teamwork and positive attitudes towards mathematics.

• The first school to win the cove­ted shield was Mikiel Anton Vassalli Junior Lyceum, Tal-Ħandaq, Qormi, which beat a team from St Joseph School, Blata l-Bajda, in the final.

• St Aloysius’ College, Birkirkara, has won the team competition of the Malta Mathematics Olympiad no less than four times.

For more trivia, see: www.um.edu.mt/think

Sound bites

• The number 3.14159... obtained by dividing the circumference of a circle by the diameter, is called pi. A beautiful mathematical result is that pi is irrational, meaning it is not an integer divided by another integer. Consequently, its decimal expansion is infinite and does not settle into a repeating pattern. Yasumasa Kana­da, who was a professor in the Department of Information Science at the University of Tokyo, Japan, until his re­tire­ment in 2015, held several world records for calculating the largest number of digits in pi. In 2002, he calculated pi to 1.2411 trillion (1,241,100,000,000) digits. In 2003, he published the number of times each of the digits 0, 1, ...9 appears in the first trillion digits of pi. Strikingly, these numbers are very close, that is, the digits are almost evenly distributed, and hence each one appears approximately one-tenth of one trillion times.

• A positive integer is a prime if it is divisible only by one and itself. Primes seemed to appear in a random fashion. In 2016, Kannan Soundararajan and Robert Lemke Oliver of Stanford University, US, surprised the mathematics world by discovering a pattern in the last digits of primes. They checked the first 100 million primes and discovered that primes tend to avoid having the same last digit as that of the last prime preceding them. For example, a prime ending in 1 was followed by a prime ending in 1 in only 18.5 per cent of the cases, which is significantly less than the expected 25 per cent (all primes greater than five end with one of the four digits 1, 3, 5 and 7, hence the 25 per cent percentage). Their paper, entitled ‘Unexpected biases in the distribution of consecutive primes’, was published in the Proceedings of the National Academy of Sciences of the United States of America in 2016.

For more science news, listen to Radio Mocha on Radju Malta 2 every Saturday at 11:05am.

Sign up to our free newsletters

Get the best updates straight to your inbox:
Please select at least one mailing list.

You can unsubscribe at any time by clicking the link in the footer of our emails. We use Mailchimp as our marketing platform. By subscribing, you acknowledge that your information will be transferred to Mailchimp for processing.