# Birmingham Popular Maths Lectures

The Birmingham Popular Maths Lectures are open to anyone with an interest in Maths, particularly those studying for A-level and above. There is no need to book just come along from 7pm for a 7.30pm start.

The series has finished for the 2013/14 academic year and will start again in September 2014.

Please contact the Outreach Officer for more information.

## Past Lectures (2013/2014)

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**11/9/13 "The Kakeya Needle Problem"**

**Professor Jon Bennett (University of Birmingham)**

In 1917 the Japanese Mathematician Soichi Kakeya raised a very simple question: what is the minimum area required to turn a line of length 1 through 180 degrees in the plane? In this lecture we discuss the very surprising answer to this question, and indicate how such problems have come to lie at the heart of modern mathematics.

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**9/10/13 "The Maths Juggler"**

**Dr Colin Wright**

Juggling has fascinated people for centuries. Seemingly oblivious to gravity, the skilled practitioner will keep several objects in the air at one time, and weave complex patterns that seem to defy analysis. In this talk the speaker demonstrates a selection of the patterns and skills of juggling while at the same time developing a simple method of describing and annotating a class of juggling patterns. By using elementary mathematics these patterns can be classified, leading to a simple way to describe those patterns that are known already, and a technique for discovering new ones. Along the way, we discover a few extra surprises...

Colin Wright graduated in Pure Mathematics at Monash University, Melbourne, before going on to get a PhD at Cambridge. While there he learned how to fire-breathe, unicycle and juggle. These days he is director of a company that specialises in software for marine radar, but takes out time to give juggling talks all over the world.

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**13/11/13 "Maths in the making of the modern world"**

**Professor Chris Budd (University of Bath)**

We live in a world dominated by technology, from the Internet to the IPad and the mobile phone to GPS. Yet how many of us realise that all of this technology is based on mathematics, and that without maths the modern world would not exist.

In this talk Professor Budd describes the maths that makes internet giants like Google function, and is behind the programming of the iPod and the mobile phone. He will also show how maths had led to the modern information revolution. No previous knowledge of maths is needed, but please bring your imagination!

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**4/12/13 "Pi, interstellar dust, and single-pixel cameras: some surprising uses for random numbers"**

**Dr Iain Styles (University of Birmingham)**

Randomly generated sequences of numbers are surprisingly useful tools that can help us perform complex calculations. In this talk, we will explore how random numbers can be used in a variety of ways: from a simple way to compute Pi, through modelling the propagation of radiation from stars through interstellar dust, to building imaging cameras that have only one pixel.

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**22/01/14 "The surprising difficulty of using mathematics in computer science"**

**Professor Achim Jung (University of Birmingham)
**

In 1959 the Noble Prize winner Eugene Wigner gave a talk with the title "The unreasonable effectiveness of mathematics in the natural sciences". A write-up is easily available on the Internet, but, briefly, Wigner argued that in the natural sciences, and in physics in particular, mathematics exhibits an "a priori" usefulness and he speculates why this should be so. In computer science we also use mathematical language and mathematical theories, but one should perhaps not speak so much of "applicability" of one to the other, but of a rich and constantly evolving relationship between the two disciplines. I will trace one instance of this relationship; that which starts with Church's lambda calculus in the 1930s and has since led to the development of programming languages such as Haskell.

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**5/2/14 "Primes and Polygons"**

**Dr John Silvester (King's College London)**

The game of constructing geometrical figures with ruler and compasses was invented by the ancient Greeks. Most people know how to construct an equilateral triangle, or a square; it is harder (but possible) to construct a regular pentagon, and impossible to construct a regular heptagon. What is going on here? There is an unexpected connection between the values of n for which a regular n-gon can be constructed, and the prime factors of n. It has to do with the Fermat primes, numbers of the form 2m + 1, where as far as we know m must be 1, 2, 4, 8 or 16. Fermat thought m could be any power of 2, but Euler showed he was wrong.

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**"100 million to 1: what can maths tell us about the Great Sperm Race?"**

**Dr David Smith (University of Birmingham)**

Reproduction is a numbers game! The average man produces over a thousand sperm every heart beat, yet only one is needed for fertilisation. Due to the pressing need for better ways to diagnose infertility, the subject is very important. This talk focuses on work bringing different areas of science together, led by Birmingham Women's Hospital, through which maths, combined with engineering and physics, are being applied to understand how sperm propel themselves through the tortuous maze of the female tract. We will look at both the fluid mechanics of microswimming and the migration of populations through complex microarchitectures, including the tantalising possibility that sperm might be guided to the egg. The guiding theme will be how maths and computing help us to understand the counterintuitive world that sperm encounter; the talk will also feature both high speed imaging of cells in microscopic mazes and human tract explants, and ‘virtual sperm’ supercomputing simulations.

## Past Lectures (2012/2013)

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**05/12/12 "How Round is Yoiur Circle?"**

**Dr Chris Sangwin (University of Birmingham)**

Mechanisms are all around us. We often take them for granted, or don't even notice they exist. Most have a long and interesting history. Almost all such mechanisms rely on rotating parts. That is, one circular part which fits inside another. These need to be made very accurately to work safely, smoothly and without wearing out. This raises a basic problem which links engineering to mathematics. How do you test if something is round? I.e., how round is your "circle"? Sounds simple? The answer to this question turns out to be much more interesting than it first appears. It involves the shape of the 50p coin, the NASA Space Shuttle Challenger explosion in 1986 and how to drill a square hole.

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**16/01/13 "How Big is Infinity?"**

**Dr Chris Good (University of Birmingham)**

Just how big is infinity? Bigger than you might think. It turns out that there are infinitely many infinities and that given any infinity there is a bigger one. In this talk we will prove that there are at least two infinities and along the way touch on ideas of Georg Cantor that split the mathematical community at the end of the 19th century.

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**6/2/13 "Mathematics Under the Lens"**

**Dr Richard Kaye(University of Birmingham)**

The first lens that successfully records straight lines in the subject as straight lines in the image was introduced simultaneously by Dallmeyer and Steinheil in 1866. Known as the "rapid rectilinear" or "aplanat" lens, it was a significant improvement on previous lenses. We will explore the geometry of transformations that preserve straight lines, and give a number of illustrations and creative techniques in photography that illustrate the use of rectilinear lenses. This talk will look at some of the geometry behind camera lenses.

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**13/3/14 "The Maths of Google"**

**Dr Richard Lissaman**

Internet search engines and video graphics are both multi-billion pound global industries. And maths is at the heart of both of them. Google depends on simultaneous equations, while the graphics behind computer animated films and games require thousands of calculations involving triangles, angles and vectors. In this session we’ll look at applications of school level mathematics in internet search engines and video games.

Richard Lissaman is Programme Leader of the Further Mathematics Support Programme. He has been a lecturer at Warwick University, and for a couple of years he also worked part time advising a computer games company in London. Richard has a PhD in algebra and is an author of maths textbooks.

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**17/4/13 "Could a Baby Robot Grow Up to Be a Mathematician?"**

**Professor Aaron Sloman**

Euclidean geometry is one of the greatest products of human minds, brought together in Euclid's Elements over two millenia ago. However, at some distant earlier time there were no geometry textbooks and no teachers. So, long before Euclid, our ancestors, perhaps while building huts, temples and pyramids, or making tools or weapons, or measuring fields, or reasoning about routes, must have noticed facts about spatial structures and processes that are not only useful, but, unlike facts of physics, chemistry and biology, are provable by reasoning, without having to keep checking that they remain true at high altitudes, or in cold weather, or on surfaces with unusual materials or colours. Without teachers to help, biological evolution must somehow have produced information-processing mechanisms that allowed ancient humans to develop the concepts, notice the relationships and discover the proofs that later humans normally encounter at school, but which we have the ability to discover for ourselves, as our ancestors did. All this suggests that normal human children have the potential to make those discoveries, under appropriate conditions. I suspect there are deep connections with competences that have evolved in other intelligent species that understand spatial structures, relationships and processes -- such as nest-building birds, squirrels working out how to get nuts from bird feeders, elephants that manipulate water, mud, sand and foliage with their trunks, and apes coping with many complex structures as they move through and feed in tree-tops. One way to demonstrate the feasibility of this conjecture is to try to design a robot that starts off with the competences of a very young child and develops in similar ways, extending those competences, and later perhaps being stimulated by the environment to make simple discoveries in Euclidean geometry -- unlike current geometric reasoning programs that use cartesian coordinate representatons of geometrical structures. How to do this is not at all obvious. There have been great advances getting computers to reason logically, algebraically and arithmetically, but the kinds of reasoning in Euclid, e.g. using diagrams, are very different. I'll discuss some of the problems and possible ways forward. Perhaps someone now studying geometry at school will one day design the first baby robot that grows up to be a self-taught robot geometer, and, like some of our ancestors, discovers for itself why the angles of a planar triangle must add up to exactly half a rotation?