Mathematics with Friends - The First Episode

# Mathematics with Friends - The First Episode

#### Age Problems

Blog by Ioanna Georgiou and illustrated by Asuka Young

The section in red comes from Season 3, Episode 18 of the TV series “Friends” created by Marta Kauffman & David Crane, and broadcasted by NBC between 1994 and 2004 and readily available on streaming channels. We use the everyday mathematical themes mentioned as our starting point, to explore the fascinating world of mathematics further.

Joey: You are 18, okay? She is 44. When you're 36, she's gonna be 88.

Frank Jr: You don't think I know that?

Thinking time - before you read on, try and answer these questions:

• What went wrong with Joey's calculation?

• How old will Alice be when Frank Jr will be 36?

Sometimes old-ish people like to say “I’m twice your age!” which may or may not be true. When are people twice somebody else’s age?

Let’s start our exploration with a case of siblings (our own mathematics characters!).

Let’s say that the oldest, Alexandra, has lived three years with exclusive access to parents, grandparents and other services. Bliss! But when she is three years old, a new baby arrives!

How can someone be even louder? As the years go by when Princess no.1 is four years old, the Non-princess (let’s face it), let’s call her Viktoria, is one. The gap seems vast! Alexandra can walk, talk, eat, even pick outfits (very important), whilst Viktoria makes up silly words.

Then a year later, Alexandra, the oldest, is five, and Viktoria, the youngest, is two and then another year later, the ages are six and three respectively. At six and three, Alexandra is triumphantly double the age of Viktoria.

From there on, the difference seems to shrink somehow. One day they will be 43 and 40 and then if they’re lucky, 97 and 94. No one thinks they’re double anyone else’s age then!

So what did go wrong with Joey’s calculation in the dialogue above?

He doubled Frank’s age from 18 to 36. So far so good. How many years would go by before Frank is 36? Well, this is easy: 36 − 18 = 18. And what happened with Alice’s age? From 44 she jumps to 88 in the same time span it took Frank to get to 36. But clearly 88 − 44 = 44. Time doesn’t double! Time passes one year a year. Simple. Or a year for every rotation of the earth around the sun. Easy.

Can we find out when will Alice be double of Frank’s age?

Let’s start with their age difference: 44 − 18 = 26. When Frank was born, she was already 26. Which means when Frank is 26, she will be 52. And that’s about it. Will not be double his age before this or after. When they met, she was clearly more than double his age. But that could happen when your parents arrange playdates for you when you are seven and one of the other children is one. Not much fun there, and seven times older! That’s heavy!

How about the parents’ age gap, then?

If when Alexandra was born a parent was 30, they will be double her age only when she is 30, and them 60. They will be multiple times her age before then, and less than double after that. If they were 40, again they will be double her age only when Alexandra is 40 and them 80.

Next steps

Check out the differences in age with your siblings, friends, aunties and uncles or grandparents! When will they be double your age? And if younger than you, when will you be double their age? Or even triple?

#### More about the Author and Illustrator - and Preorder the Book

Asuka Young, the amazing illustrator I collaborated with for Mathematical Adventures! and Peculiar Deaths of Famous Mathematicians has livened up the dialogues with her illustrations! And we can’t wait to see this material transforming into a book in the end of this series. You can even pre-order it at a special price if you’d like! See here for more details.

Get in touch with me at https://ioannageorgiou.com/ for the mathsy side of things and with Asuka using the handle @asuka_young for viewing more fantastic illustrations.