Whilst not part of the KS3 or KS4 curriculum, infinity is undoubtedly a fascinating concept. From Borges’ infinite library to Hilbert’s paradoxical hotel, there are many ways to help your students think deeply about infinity and enhance mathematical understanding beyond the classroom.
The Library of Babel
In Jorge Luis Borges’ short story, The Library of Babel, he describes a library that consists of a set of books that all have 410 pages, 40 lines per page and 80 letters per line. This library contains every possible combination of the 26 letters of the alphabet.
Just imagine that for a moment…every possible arrangement of letters.
In this library, you’ll find not only the biographies and autobiographies of everyone who has ever lived but also those who will ever live and those who have never lived. There are details of everything that has ever happened, everything that will ever happen and everything that has never happened.
Every book that has ever been written is in the library. The complete works of Shakespeare, Joyce and Proust are all lost among books without a single legible word in them.
Yet despite this unimaginable scope, there’s still a finite number of books.
It’s no wonder students and adults alike are fascinated by this concept of infinity. It is just so (un)imaginably big, yet reducible to a single word…infinity.
Hilbert’s Hotel
Your sixth form students might also enjoy checking into Hilbert’s Hotel, a hotel with an infinite number of rooms. What do you do if more guests arrive? What about a coachload with an infinite number of guests? How about an infinite number of coaches with an infinite number of guests? It’s not just the Hotel manager with a headache!
Explore this Numberphile video on Infinity Paradoxes to learn more:
Exploring Infinity With Your Students
Though infinity isn’t a formal part of the KS3 or KS4 curriculum, it offers an exciting way to enrich students’ learning. The AMSP has some fantastic resources for those eager to explore such thought-provoking topics.
Check out Fractals as part of our Maths Club Activities and explore ideas of infinity while drawing some beautiful shapes. How can a shape have an infinite perimeter yet a finite area? This resource is ideal for KS3 and KS4 students.
Explore these resources below:
Fractals
Fractals allow us to challenge our notion of infinity while drawing some beautiful shapes. This activity explores Koch’s Curve and the Sierpinski Triangle.
Maths Club Activities
These resources are designed to support the many Maths Clubs that schools run across the country. Each activity is fully resourced and accessible to all 11-16 students at different levels.
This article was written by Jerome Foley – Area Coordinator for Nottingham and Nottinghamshire.