Practice English Listening A2 Exercises – Math and Technology: Radio program on the Fibonacci sequence

A

5 4 3 1 2

B

Answers will vary.

1   flowers, pinecones, seashells

2   2 hands, 5 fingers, 3 knuckles

3   Leonardo da Vinci’s paintings

4   patterns in Bach’s music

C

1 T   2 F   3 F   4 T   5 T   6 F   7 F   8 T

A = Host, B = Dr. James Quist

A:   This is Pat Lee and you’re listening to Math World. Now, here’s a question: Can you guess how the human hand, the petals of certain kinds of flowers, and even some famous paintings could be related mathematically? Well, if you have no idea, our question of the day, from listener Lucy Warrick, in Rhode Island, will help you. Ms. Warrick asks, “I’ve heard a lot about the Fibonacci sequence lately. What exactly is it?”

For an answer, we contacted Professor of Mathematics, Dr. James Quist. Hello, Dr. Quist. Can you tell us a little about the Fibonacci sequence to answer Ms. Warrick’s question?

B:   Well, that’s a great question, especially since the sequence is around us in so many forms, and many people have no idea about it. It’s really very intriguing once you’re aware of it.

First, what the sequence is. It’s a series of numbers, and in the sequence, each number is the sum of the preceding two numbers. In other words, you add two numbers together to get the next one. Let’s look at the start of it. The numbers are one, one, two, three, five, and eight. So, if we add the first two numbers – one and one – we get two, which is the third number. Then, one and two equal three, which is the fourth number. Then, two and three equal five, which is the fifth number. And so it continues.

A:   So, let’s see … each number is the sum of the previous two numbers, and the sequence can just go on and on?

B:   Yes, that’s right. And, what’s so amazing about this is that the sequence shows up around us in so many ways. It appears in the natural world. Natural forms tend to reproduce the sequence. For example, flowers, pinecones, or seashells. Look at the petals on a flower. They’re more likely to be five petals, than four. The spirals in a seashell also involve numbers from the sequence. It’s not as easy to see as with flowers, but the measurements of the spiral are numbers of the sequence. Some people even mention the human hand when talking about the sequence. We have two hands, each of these has five fingers, and each finger has three parts separated by two knuckles. All of these are numbers in the sequence. Maybe it’s just a coincidence, or maybe not.

And, it’s not just in the natural world; it’s also in the art world. It appears in a lot of art. Probably, the most famous is in the work of Leonardo da Vinci. You see a lot of spirals in his painting, and spirals are the form most associated with the Fibonacci sequence. It also appears in music. One of Bach’s pieces is based on this sequence, in the way the musical patterns repeat. Now, it’s not clear whether Bach did this consciously or not.

A:   Interesting. Who discovered all this?

B:   It was discovered by a mathematician in Italy in the early 1200s. His name was Leonardo of Pisa, but he called himself Fibonacci because his father’s name was Bonacci. Anyway, he was an extraordinary mathematician. He actually introduced the decimal system to other mathematicians of the time.

A:   So mathematicians have known about the sequence for a long time?

B:   Yes, Now, your listener says that she’s heard a lot lately about the Fibonacci sequence. It seems like interest in this area kind of comes and goes in popularity. Lately, it has been more popular. I think it’s great. It’s fascinating, and if it gets people interested in math and numbers, then all the better.

A:   It is fascinating. Thank you so much, Dr. Quist.

B:   You’re welcome.