These are the show notes for episode 56 of the Travels in a Mathematical World Podcast. 56 is the 6th tetrahedral number, meaning it is the sum of the first six triangular numbers. More about tetrahedral numbers from thesaurus.maths.org.
This week on the podcast I spoke to Edmund Harriss of the University of Leicester, and we discussed a range of topics around enthusing people about mathematics and how mathematical ideas are developed and taught.
Ptolemy Mathcards were designed by Edmund and Chaim Goodman-Strauss. You can find out about the creation and development of mathematical ideas by investigating the history of mathematics. A good place to start is The British Society for the History of Mathematics. If you are interested in the use of history in mathematics teaching, try the BSHM Education site.
You can find out more about Edmund's work in tiling patterns and maths outreach by listening to episode 55 of the podcast. I recommend Edmund's blog Maxwell's Demon, and following Edmund on Twitter as @Gelada.
You can find out more about the IMA by visiting http://www.ima.org.uk/student/. You can find out more about what I do by reading this blog, by following me on Twitter or visiting peterrowlett.net. Join the Travels in a Mathematical World Podcast Facebook Fan Page.
Sunday, 28 February 2010
Sunday, 21 February 2010
Podcast: Episode 55 - Edmund Harriss, Tilings, motivations and Street Maths
These are the show notes for episode 55 of the Travels in a Mathematical World Podcast. 55 is the largest triangular number in the Fibonacci sequence. More about 55 from Number Gossip.
This week on the podcast I spoke to Edmund Harriss of the University of Leicester, who speaks about his research area of tiling patterns and how this leads him into maths outreach.
Edmund contributes to a Tilings Encyclopedia. You can read about medieval Islamic tilings in New Scientist. There is a gallery of Escher tilings at Mathematical Imagery. You can find out more about Escher on the M.C. Escher website, or by reading the Escher biography at the MacTutor History of Mathematics archive. You can read about Penrose tilings in the Tilings Encyclopedia and read a biography of Penrose at MacTutor.
Edmund's Royal Society exhibition has a website: "How do shapes fill space?" You can find out more about Street Maths by viewing Edmund's slides "Street Maths". You can read Marcus du Sautoy on motivating interest in mathematics in the Guardian article "The secret life of numbers". Edmund mentions a meeting he ran at Leicester, "Talking to teachers".
I recommend Edmund's blog Maxwell's Demon, and following Edmund on Twitter as @Gelada.
You can find out more about the IMA by visiting http://www.ima.org.uk/student/. You can find out more about what I do by reading this blog, by following me on Twitter or visiting peterrowlett.net. Join the Travels in a Mathematical World Podcast Facebook Fan Page.
This week on the podcast I spoke to Edmund Harriss of the University of Leicester, who speaks about his research area of tiling patterns and how this leads him into maths outreach.
Edmund contributes to a Tilings Encyclopedia. You can read about medieval Islamic tilings in New Scientist. There is a gallery of Escher tilings at Mathematical Imagery. You can find out more about Escher on the M.C. Escher website, or by reading the Escher biography at the MacTutor History of Mathematics archive. You can read about Penrose tilings in the Tilings Encyclopedia and read a biography of Penrose at MacTutor.
Edmund's Royal Society exhibition has a website: "How do shapes fill space?" You can find out more about Street Maths by viewing Edmund's slides "Street Maths". You can read Marcus du Sautoy on motivating interest in mathematics in the Guardian article "The secret life of numbers". Edmund mentions a meeting he ran at Leicester, "Talking to teachers".
I recommend Edmund's blog Maxwell's Demon, and following Edmund on Twitter as @Gelada.
You can find out more about the IMA by visiting http://www.ima.org.uk/student/. You can find out more about what I do by reading this blog, by following me on Twitter or visiting peterrowlett.net. Join the Travels in a Mathematical World Podcast Facebook Fan Page.
Thursday, 18 February 2010
Countability and uncountability in Facebook groups
If you use Facebook, you may be familiar with the groups based on the 'million march'-principle, who are trying to get to a certain number of members to affect some change.
A lot of these groups are outright silly, or based around issues unlikely to drum up the enthusiasm of the masses. A quick search finds individuals offering to give up smoking, get a tattoo and eat their keyboard. Groups range from the unbelievable "If this group reaches a million, I'll name my kid after a diacritical mark", to the much more grounded in reality* "If this group reaches 1,000,0000 NOTHING will happen".
(* in concept, although the representation of numbers leaves something to be desired)
Then there are the more serious campaigns, like "One Million Strong for Barack", "1 Million Strong For Same-Sex Marriage Throughout The Entire United States" and "One Million Strong for the Separation of Corporation and State". These are centres for activity on serious campaigns and tend to have more members (the first two have hit their mark).
Anyway, earlier this week I saw an xkcd cartoon suggesting the Facebook group of a Tautology Club be called "If 1,000,000 people join this group, it will have 1,000,000 people in it". And today I was invited to join "Aleph-One Strong for the Generalized Continuum Hypothesis!" by Tony Mann, who wrote:
On the group Wall, member Justin Howard Wilson has a way to check on the progress of the mission: "Are we there yet? *Counts members* Crap, I'm still able to count them!"
This also reminds me of a group I saw quite a while ago, "If this group reaches 4,294,967,296 it might cause an integer overflow".
A lot of these groups are outright silly, or based around issues unlikely to drum up the enthusiasm of the masses. A quick search finds individuals offering to give up smoking, get a tattoo and eat their keyboard. Groups range from the unbelievable "If this group reaches a million, I'll name my kid after a diacritical mark", to the much more grounded in reality* "If this group reaches 1,000,0000 NOTHING will happen".
(* in concept, although the representation of numbers leaves something to be desired)
Then there are the more serious campaigns, like "One Million Strong for Barack", "1 Million Strong For Same-Sex Marriage Throughout The Entire United States" and "One Million Strong for the Separation of Corporation and State". These are centres for activity on serious campaigns and tend to have more members (the first two have hit their mark).
Anyway, earlier this week I saw an xkcd cartoon suggesting the Facebook group of a Tautology Club be called "If 1,000,000 people join this group, it will have 1,000,000 people in it". And today I was invited to join "Aleph-One Strong for the Generalized Continuum Hypothesis!" by Tony Mann, who wrote:
This group wants Aleph-1 members so it can test the Continuum Hypothesis. It already has almost 700, so only another Aleph-1 are needed. As the group says, invite all your friends to join, but if you only have finitely many friends you're no use to them.
On the group Wall, member Justin Howard Wilson has a way to check on the progress of the mission: "Are we there yet? *Counts members* Crap, I'm still able to count them!"
This also reminds me of a group I saw quite a while ago, "If this group reaches 4,294,967,296 it might cause an integer overflow".
Sunday, 14 February 2010
Podcast: Episode 54 - Maths news with Sarah Shepherd
These are the show notes for episode 54 of the Travels in a Mathematical World Podcast. 54 is the number of colored squares on a Rubik's cube. More about 54 from Number Gossip.
This week on the podcast I met Sarah Shepherd, PhD student at the University of Nottingham and Editor of iSquared Magazine, and we discussed some maths news. Links to all the articles we mentioned are below.
Fabrice Bellard claims to have calculated Pi to 2.7 trillion digits on a desktop computer using a highly efficient algorithm. Read "Pi calculated to 'record number' of digits" from the BBC.
Mathematical Ethnographies, a film project at the University of Bristol, aims to explore how mathematicians think and work, their passion for the subject, what their motivations are, and how they view themselves. Read the press release "New films explore the pain and the pleasure of maths".
The list of books recommended to me via Twitter for a 13-year old keen mathematician is on my blog as Reading list for a keen 13 year old mathematician.
Marcus du Sautoy chooses 5 books which "reveal the beauty of mathematics" in an interview with The Browser. Read "The Beauty of Maths".
Marcus du Sautoy has been awarded OBE for services to science. Read "New Year Honours 2010" from the University of Oxford.
The Mandelbulb is a 3d interpretation of an object similar to the Mandelbrot set. See images from the Mandelbulb on the page entitled "Mandelbulb: The Unravelling of the Real 3D Mandelbrot Fractal" and read an article on how it was done in the New Scientist as "The Mandelbulb: first 'true' 3D image of famous fractal".
An exhibition, 1001 Inventions, at the Science Museum, London as part of an exhibition aimed at bringing Islamic scientists to greater public recognition. Read "Elephant clock trumpets golden age of ancient Islamic science" in the Times. Noel-Ann Bradshaw covered the life and works of the Islamic scholar al-Kharazmi in podcast Episode 17 - History with Noel-Ann Bradshaw - al-Kharazmi.
The number of people joining teacher training courses in England this year are up. Read "Trainee teacher targets exceeded" from the BBC.
Girls are just as good at maths as boys but they are too shy to realise their talents, new research has found. Read "Girls 'too shy' to shine in maths" in the Telegraph.
Schools are using drama, role-play, music and dance to get children interested in subjects such as maths and science, according to Ofsted. Read "Schools using dance and fashion to get bored pupils interested in maths" in the Telegraph.
The Guardian has a special report on how to build up confidence in teaching and learning maths, "Do the maths". This includes articles on Maths using Google Maps, video games, Maths Careers website relaunch, Chartered Mathematics Teacher, Self-evaluation tools for maths teachers, series of short interviews on how maths made careers, including Simon Singh, Carol Vorderman, Johnny Ball and Kate Bellingham.
The MathsCareers website is available via www.mathscareers.org.uk.
Professor Robin Sharp has spent a year perfecting the design for an autonomous unicycle. Read "Design for an autonomous unicycle".
The way fungus-like slime moulds grow could help engineers design wireless communication networks. Read "Engineers 'can learn from slime'" from the BBC. Someone else who is keen on modern engineering methods learning from nature is Adrian Bowyer, who talks about this in episode 9 and episode 10.
Woolworths Stores: read Matt Parker's satire "Locations of Ancient Woolworths Stores follow Precise Geometrical Pattern".
You can find out about Mathematics Today on the IMA website.
For more about iSquared Magazine visit the iSquared Magazine Website.
You can find out more about the IMA by visiting http://www.ima.org.uk/student/. You can find out more about what I do by reading this blog, by following me on Twitter or visiting peterrowlett.net. Join the Travels in a Mathematical World Podcast Facebook Fan Page.
This week on the podcast I met Sarah Shepherd, PhD student at the University of Nottingham and Editor of iSquared Magazine, and we discussed some maths news. Links to all the articles we mentioned are below.
Fabrice Bellard claims to have calculated Pi to 2.7 trillion digits on a desktop computer using a highly efficient algorithm. Read "Pi calculated to 'record number' of digits" from the BBC.
Mathematical Ethnographies, a film project at the University of Bristol, aims to explore how mathematicians think and work, their passion for the subject, what their motivations are, and how they view themselves. Read the press release "New films explore the pain and the pleasure of maths".
The list of books recommended to me via Twitter for a 13-year old keen mathematician is on my blog as Reading list for a keen 13 year old mathematician.
Marcus du Sautoy chooses 5 books which "reveal the beauty of mathematics" in an interview with The Browser. Read "The Beauty of Maths".
Marcus du Sautoy has been awarded OBE for services to science. Read "New Year Honours 2010" from the University of Oxford.
The Mandelbulb is a 3d interpretation of an object similar to the Mandelbrot set. See images from the Mandelbulb on the page entitled "Mandelbulb: The Unravelling of the Real 3D Mandelbrot Fractal" and read an article on how it was done in the New Scientist as "The Mandelbulb: first 'true' 3D image of famous fractal".
An exhibition, 1001 Inventions, at the Science Museum, London as part of an exhibition aimed at bringing Islamic scientists to greater public recognition. Read "Elephant clock trumpets golden age of ancient Islamic science" in the Times. Noel-Ann Bradshaw covered the life and works of the Islamic scholar al-Kharazmi in podcast Episode 17 - History with Noel-Ann Bradshaw - al-Kharazmi.
The number of people joining teacher training courses in England this year are up. Read "Trainee teacher targets exceeded" from the BBC.
Girls are just as good at maths as boys but they are too shy to realise their talents, new research has found. Read "Girls 'too shy' to shine in maths" in the Telegraph.
Schools are using drama, role-play, music and dance to get children interested in subjects such as maths and science, according to Ofsted. Read "Schools using dance and fashion to get bored pupils interested in maths" in the Telegraph.
The Guardian has a special report on how to build up confidence in teaching and learning maths, "Do the maths". This includes articles on Maths using Google Maps, video games, Maths Careers website relaunch, Chartered Mathematics Teacher, Self-evaluation tools for maths teachers, series of short interviews on how maths made careers, including Simon Singh, Carol Vorderman, Johnny Ball and Kate Bellingham.
The MathsCareers website is available via www.mathscareers.org.uk.
Professor Robin Sharp has spent a year perfecting the design for an autonomous unicycle. Read "Design for an autonomous unicycle".
The way fungus-like slime moulds grow could help engineers design wireless communication networks. Read "Engineers 'can learn from slime'" from the BBC. Someone else who is keen on modern engineering methods learning from nature is Adrian Bowyer, who talks about this in episode 9 and episode 10.
Woolworths Stores: read Matt Parker's satire "Locations of Ancient Woolworths Stores follow Precise Geometrical Pattern".
You can find out about Mathematics Today on the IMA website.
For more about iSquared Magazine visit the iSquared Magazine Website.
You can find out more about the IMA by visiting http://www.ima.org.uk/student/. You can find out more about what I do by reading this blog, by following me on Twitter or visiting peterrowlett.net. Join the Travels in a Mathematical World Podcast Facebook Fan Page.
Thursday, 11 February 2010
Truchet, Braille and Euler
In going through a hard drive I came across some playing around I did a couple of years ago with Truchet tilings which I thought I would share with you here.
I came across Truchet tilings in a talk a couple of years ago by Cameron Browne to the London Knowledge Lab's Maths-Art Seminar Series. (Sébastien Truchet is the first person I have thought would be in but found not to be in The MacTutor History of Mathematics archive).
To cut an interesting story short, Truchet tiles come in two forms which can be represented as:
These are then combined to form interesting curves, thus:
You can colour these tiles, making four visually different tiles:
So the pattern becomes like:
Or the inverse.
So. if you think about it, the two types of tile can be used to represent two points - for example binary data - using the two symbols and .
At the time I was playing around with Braille notations for mathematics. Braille characters are made up of 3 rows of 2 cells each (or, in some advanced forms, 4 rows of 2 cells). Cells contain raised dots or don't and the pattern is used to feel which character is which. Representing raised dots as black dots and, then the Braille character for, say, "m" is:
If we take this as a pattern of 1s (raised dots) and 0s (absence of dots) then this is:
If we take one Truchet symbol to be a raised dot and the other to be the absence of such a dot then we can represent a pattern of dots as a Truchet tiling. So, for example take to be a raised dot and to be the absence. Then a British Braille "m" is:
Or a coloured version:
Okay, so then I looked for something suitable to encode this way. I chose Euler's identity. Taking to be a raised dot and to be the absence I encoded the identity using the BAUK Braille Mathematics Notation and coloured this using one colouring or the other, chosen aesthetically. This gives (click to enlarge):
Finally, I gave this a bit of a colouring and eroded the shapes in a way I thought looked appealing. Please click on the following to enlarge:
Really this is all very contrived but I quite like it. Of course, there is something contrary to intentions about generating a visually appealing image from a tactile representation. I think the pattern is attractive and the hidden meaning, and particularly of such a beautiful formula, I think adds something to the effect.
I came across Truchet tilings in a talk a couple of years ago by Cameron Browne to the London Knowledge Lab's Maths-Art Seminar Series. (Sébastien Truchet is the first person I have thought would be in but found not to be in The MacTutor History of Mathematics archive).
To cut an interesting story short, Truchet tiles come in two forms which can be represented as:
These are then combined to form interesting curves, thus:
You can colour these tiles, making four visually different tiles:
So the pattern becomes like:
Or the inverse.
So. if you think about it, the two types of tile can be used to represent two points - for example binary data - using the two symbols
and .At the time I was playing around with Braille notations for mathematics. Braille characters are made up of 3 rows of 2 cells each (or, in some advanced forms, 4 rows of 2 cells). Cells contain raised dots or don't and the pattern is used to feel which character is which. Representing raised dots as black dots and, then the Braille character for, say, "m" is:
If we take this as a pattern of 1s (raised dots) and 0s (absence of dots) then this is:
1 1
0 0
1 0
0 0
1 0
If we take one Truchet symbol to be a raised dot and the other to be the absence of such a dot then we can represent a pattern of dots as a Truchet tiling. So, for example take
to be a raised dot and to be the absence. Then a British Braille "m" is:Or a coloured version:
Okay, so then I looked for something suitable to encode this way. I chose Euler's identity. Taking
to be a raised dot and to be the absence I encoded the identity using the BAUK Braille Mathematics Notation and coloured this using one colouring or the other, chosen aesthetically. This gives (click to enlarge):
Finally, I gave this a bit of a colouring and eroded the shapes in a way I thought looked appealing. Please click on the following to enlarge:
Really this is all very contrived but I quite like it. Of course, there is something contrary to intentions about generating a visually appealing image from a tactile representation. I think the pattern is attractive and the hidden meaning, and particularly of such a beautiful formula, I think adds something to the effect.
Tuesday, 9 February 2010
Carnival of Mathematics
I have recently become aware of the Carnival of Mathematics, a blog carnival operated by Mike Croucher. A blog carnival is a roaming, regular series of blog posts on a particular topic that points to content on other blogs. In this case, the Carnival of Mathematics website has the following description of the content:
The website lists Carnival posts going back to Feb 2007. The most recent Carnival post at time of writing is number 62 at The Endeavour.
Anyway, I have signed up to host the 67th Carnival of Mathematics in July. Watch this space!
Pure or Applied, Good or Bad, in Science or in Social Science, Academic or PopularMike's Twitter feed for the Carnival describes it as "a monthly celebration of the mathematics blogging community. Hosted by a different math blogger each month."
Everything math-related goes in here: proofs, explanations of basic concepts, puzzles, writings about math education, mathematical anecdotes, refutations of bad math, applications of math, reviews of popular math... Note that sufficiently mathematized portions of other disciplines, especially physics and computer science, are acceptable.
The website lists Carnival posts going back to Feb 2007. The most recent Carnival post at time of writing is number 62 at The Endeavour.
Anyway, I have signed up to host the 67th Carnival of Mathematics in July. Watch this space!
Saturday, 6 February 2010
Podcast: Episode 53 - Robert Harter - Water waves
These are the show notes for episode 53 of the Travels in a Mathematical World Podcast. 53 is prime, the smallest multidigit balanced prime: primes which are the averages of their prime neighbours. More about 53 from Number Gossip.
Robert Harter talks about his PhD research at the University of Manchester into linear water wave problems. You can read a paper by Robert and others on this topic as "The effect of surface tension on trapped modes in water-wave problems". Prof. I. David Abrahams talks about problems in this area in an interview on his website. There is a lot of information on different water wave problems at Loughborough.
You can find out more about the IMA by visiting http://www.ima.org.uk/student/. You can find out more about what I do by reading this blog, by following me on Twitter or visiting peterrowlett.net. Join the Travels in a Mathematical World Podcast Facebook Fan Page.
Robert Harter talks about his PhD research at the University of Manchester into linear water wave problems. You can read a paper by Robert and others on this topic as "The effect of surface tension on trapped modes in water-wave problems". Prof. I. David Abrahams talks about problems in this area in an interview on his website. There is a lot of information on different water wave problems at Loughborough.
You can find out more about the IMA by visiting http://www.ima.org.uk/student/. You can find out more about what I do by reading this blog, by following me on Twitter or visiting peterrowlett.net. Join the Travels in a Mathematical World Podcast Facebook Fan Page.
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