Off the shelf Masterclass The Special Number rigb.org @Ri_Science Image credits: Tim Mitchell

Quadrilaterals: starter activity Use your sheet of circles to draw as many different quadrilaterals as you can. How many have you found? Have you found them all? Discuss your findings with your neighbour. https://nrich.maths.org/962

First we have to decide whether reflections and rotations count as the same shape or different shapes I have decided that they do not count as new solutions I have found 8 unique solutions I have laid them out in this order to work systematically, and to show that I have thought of all possibilities

Off the shelf Masterclass The Special Number rigb.org @Ri_Science Image credits: Tim Mitchell

The Royal Institution Our vision is: A world where everyone is inspired to think more deeply about science and its place in our lives. The Ri is a science communication charity which has been around since 1799. We’ve got a huge amount of history and lots of famous scientists lived and worked at the Ri. Most importantly, we’ve always been about communicating science to the general public – and that’s something we still do today. We do talks and activities for the public as well as with schools all across the UK. Image credits: Tim Mitchell

Royal Institution activities Online videos & activity resources National education programmes (including Celebration Day 6/7/19) Membership London-based: Talks and shows Holiday workshops Family fun days Faraday Museum Here are some of the things that the Ri does today. We especially have lots going on in London, so if you enjoy your Masterclasses there are a range of holiday workshops at the Ri which you might like to take part in. Image credits: The Royal Institution, Paul Wilkinson, Katherine Leedale

The CHRISTMAS LECTURES The CHRISTMAS LECTURES are the Ri’s most famous activity and are televised on the BBC. The first maths lectures by Prof. Sir Christopher Zeeman in 1978 started off the Masterclass programme! Christmas Lecturers include Michael Faraday, David Attenborough, Carl Sagan, Richard Dawkins, Alison Woollard, Saiful Islam & Alice Roberts Begun by Michael Faraday in 1825, the CHRISTMAS LECTURES are now broadcast on UK television every December and have formed part of the British Christmas tradition for generations. The Lectures have been broadcast on TV since 1936 – we think they were the very first science programme on television. The theme changes every year, with the Lectures delivered by an expert in their field. Many world-famous scientists have given the Lectures since 1925, including David Attenborough, Carl Sagan, Richard Dawkins, and our latest Lecturer Sophie Scott. You can watch all of the recent CHRISTMAS LECTURES on our website, along with many of the older ones – and more are going online all the time. Ri members and UK schools can apply for tickets to see them being filmed live – but no adults can attend without someone aged 11-17 accompanying them! To find out more about the Lectures (or Ri Membership) visit our website, www.rigb.org. The first mathematics CHRISTMAS LECTURES were not until 1978, and were delivered by Professor Sir Christopher Zeeman. They were extremely popular and demonstrated all sorts of mathematical concepts, including mathematical proof – some of which you will see in your Masterclasses. In fact, the lectures were so popular that they started off the Masterclass programme and Christopher Zeeman delivered many of the sessions in the first few series of workshops in London. The most recent maths-themed CHRSITMAS LECTURES were delivered by Marcus Du Sautoy in 2006. Watch Prof Sir Christopher Zeeman’s 1978 CHRISTMAS LECTURES: http://www.rigb.org/christmas-lectures/watch/1978/mathematics-into-pictures Watch Marcus du Sautoy’s 2006 CHRISTMAS LECTURES: http://www.rigb.org/christmas-lectures/watch/2006/the-num8er-my5teries/lecture-1   Image credits: BBC, Ri

Royal Institution videos CHRISTMAS LECTURES – on the Ri website We have a huge video channel on YouTube – if you have five minutes or five hours, there is something to interest you if you like science and maths. We make short videos showing a variety of experiments and the science behind the everyday, animations on interesting topics and we film many of our talks in London. We also have a special series called ExpeRimental which is mainly for parents and carers, or older brothers and sisters, all about doing science experiments at home with their children or younger siblings. As has been mentioned, recent CHRISTMAS LECTURES are available on the Ri website alongside select past Christmas Lectures – more are being digitised all the time. To watch our videos you can search for the Royal Institution on YouTube.  We hope that you will be able to find lots of fascinating things to watch and to help you continue your interest in science and maths once your Masterclass series has finished.

Royal Institution videos CHRISTMAS LECTURES – on the Ri website Ri on YouTube – experiments, videos & talks for all ages We have a huge video channel on YouTube – if you have five minutes or five hours, there is something to interest you if you like science and maths. We make short videos showing a variety of experiments and the science behind the everyday, animations on interesting topics and we film many of our talks in London. We also have a special series called ExpeRimental which is mainly for parents and carers, or older brothers and sisters, all about doing science experiments at home with their children or younger siblings. As has been mentioned, recent CHRISTMAS LECTURES are available on the Ri website alongside select past Christmas Lectures – more are being digitised all the time. To watch our videos you can search for the Royal Institution on YouTube.  We hope that you will be able to find lots of fascinating things to watch and to help you continue your interest in science and maths once your Masterclass series has finished.

Royal Institution videos CHRISTMAS LECTURES – on the Ri website Ri on YouTube – experiments, videos & talks for all ages ExpeRimental – science experiments at home We have a huge video channel on YouTube – if you have five minutes or five hours, there is something to interest you if you like science and maths. We make short videos showing a variety of experiments and the science behind the everyday, animations on interesting topics and we film many of our talks in London. We also have a special series called ExpeRimental which is mainly for parents and carers, or older brothers and sisters, all about doing science experiments at home with their children or younger siblings. As has been mentioned, recent CHRISTMAS LECTURES are available on the Ri website alongside select past Christmas Lectures – more are being digitised all the time. To watch our videos you can search for the Royal Institution on YouTube.  We hope that you will be able to find lots of fascinating things to watch and to help you continue your interest in science and maths once your Masterclass series has finished.

Quadrilaterals: starter activity Use your sheet of circles to draw as many different quadrilaterals as you can. How many have you found? Have you found them all? Discuss your findings with your neighbour. https://nrich.maths.org/962

First we have to decide whether reflections and rotations count as the same shape or different shapes I have decided that they do not count as new solutions I have found 8 unique solutions I have laid them out in this order to work systematically, and to show that I have thought of all possibilities

Locus of a point Rule: Put a central white counter on the table Choose another colour, and pick up 12 of that colour Place a coloured counter so that it is 10 cm from the white counter Place another of your coloured counters so that it is also 10 cm from the white counter Continue to place your coloured counters one by one so that they are all 10 cm from the white counter What shape have you made? Write down all the special words which you know which go with this shape.

Circle vocabulary!

Circle vocabulary Circle Vocabulary c e _ t _ e r a _i _ s c _ o _ d _ i a _ e t _ r c _ r c _ m _ e _ e _ c _ t _ n _ e n t a _ c s e _ t _ r _ e _ m e _ t Circle Vocabulary 1.Fill in the blank letters in the words 2.Label the words on the circle diagram

Circle vocabulary Circle Vocabulary c e n t r e r a d i u s c h o r d d i a m e t e r c i r c u m f e r e n c e t a n g e n t a r c s e c t o r s e g m e n t Circle Vocabulary 1.Fill in the blank letters in the words 2.Label the words on the circle diagram

Investigating circles Choose a circular object or a printed circle Measure and record the diameter, using the ruler, and estimating as carefully as possible where the diameter is by looking for the line that cuts the circle in half. Measure and record the circumference, using the string, and then measuring on the ruler or metre ruler Add your measurements to the spreadsheet What patterns do you notice?

Investigating circles

Break followed by randomness!

π All about Pronounced “pie”, spelt “pi” Known for thousands of years: only named in 17th century Irrational Non- terminating, non recurring decimal

π History of “The Nautilus was stationary, floating near a mountain which formed a sort of quay. The lake then supporting it was a lake imprisoned by a circle of walls, measuring two miles in diameter and six in circumference.”

How random is pi? What does “random” mean?? Write down on your scrap paper your estimate of the 2000th digit of pi. What is the chance it is: a 4? Or a 9? How many possibilities are there? So what is the chance of a particular number? If I have 100 random digits, how many 3s would I expect to have? In the first 2000 digits of ϖ how many 3s?

How random is pi? Let’s extend this idea to digit pairs How many different digit pairs are there? So what is the probability of a digit pair being chosen? Choose a digit pair and write it on the top of your copy of ϖ (first 2000 digits) Go through and count how many times your digit pair appears: Highlight it when it you find it. Think about the end/start of lines. Use you ruler to help keep track In the first 2000 digits of ϖ how many times would you expect your digit pair to appear?

How random is pi?

How random is pi?

How many digits of pi do we know? https://www.youtube.com/watch?v=5ykGnwN2f14

Find your birthday…or phone number… As ϖ is random and never ending it will contain your birthday and your phone number somewhere, if we look far enough Can you find the first possible birthday in ϖ? Is your birthday in the first 2000 digits of ϖ?

Find your pi day http://www.mypiday.com/

We hope you have enjoyed exploring pi with us! What questions do you have? Any unanswered questions can be written down and emailed to “Ask the Ri Masterclass Team” using this email masterclasses@ri.ac.uk We don’t know all the answers instantly, but we will find out and get back to you before the next Masterclass. Any comments you have about what you enjoyed or what you’d like to do more of can be written on the post-it note and handed in. Don’t forget to collect any questions which arise, and email them to the Masterclass team at the Royal Institution: masterclasses@ri.ac.uk   We will send you answers as soon as possible. Then these can be reported back to the children at their next Masterclass session. In this way you cannot be “caught out” by a question. It also demonstrates the point that not everything in maths is known, but some questions need time and research to find answers sometimes, and sometimes the answer has not been found by anyone yet, of course! Maybe our Masterclass students will be the ones who solve the problem when they are older?

What else can I do to extend my knowledge of pi?? Article about ϖ Write your own mnemonic https://nrich.maths.org/2490 https://www.math.hmc.edu/funfacts/ffiles/10001.2-8.shtml Watch a video about measuring pi with pies Find your piday! This slide could be printed and given out as a nice “take home” activity suggestion. http://www.mypiday.com/ https://www.youtube.com/watch?v=ZNiRzZ66YN0