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Martin Gardner
I was given a Martin Gardner book as a birthday present
when I was 15. When I unwrapped it, I wasn’t particularly
pleased. A year later, as boredom set in over the
summer holidays, I picked it up again and got hooked –
just in time for the sixth form. Martin Gardner didn’t
consider himself a mathematician, but as a communicator
of mathematics and as an advocate of the pleasure
obtained from understanding mathematical ideas, I think
he was second to none. This session will discuss his life
and work and will include ideas for classroom activities
to help get your students hooked on maths.
Martin Gardner
1914 - 2010
WARNING Martin Gardner has turned dozens of
innocent youngsters into Math
professors and thousands of Math
professors into innocent youngsters
Persi Diaconis
Timeline
• 1914: Born Tulsa, Oklahoma – son of an oil
geologist
• 1929: Published first article, about a magic
trick, in the magazine of the Society of
American magicians
• 1936: Bachelor’s degree in Philosophy,
University of Chicago, Early jobs as
reporter/writer
• 1941-45: Yeoman in US Navy
• Late 1940s: Moved to NY, writer and designer,
Humpty Dumpty magazine
Timeline
• 1950 - 1979 Hasting on Hudson, NY, Euclid
avenue
• 1952: Married Charlotte Greewald (2 sons)
• 1956: First Scientific American ‘Mathematical
Games’ article published
• 1960: ‘Annotated Alice’ published – has sold
over a million copies
• 1941-45: Yeoman in US Navy
• 1979: Semi-retired, moved to Hendersonville,
North Carolina
Timeline
• 1981: Final Scientific American ‘Mathematical
Games’ article (almost 300 in total)
• 1993: First ‘gathering for Gardner event, now
held in every even numbered year – devoted
to Gardner’s writings in recreational maths,
magic, puzzles, and philosophy
• 2002: Returned to live in Oklahoma, near
family
• 2010: Died, aged 96
• 2013: Autobiography ‘Undiluted Hocus-Pocus’
published posthumously
Summary?
• Writer: (wrote more than 100 published books and
hundreds of articles on books on the subjects of
mathematics, skepticism, literature, magic, and
religion)
• Friends with, and admired by many of the great
mathematicians and thinkers of the 20th century,
including John Conway, Piet Hein, Roger Penrose, Carl
Sagan, M.C. Escher, Douglas Hofstadter, Stephen J.
Gould, W.H. Auden, Arthur C. Clarke, Isaac Asimov,
Richard Dawkins, Noam Chomsky, Salvador Dali
John Conway described him as “the most learned man I
have ever met.”
Summary?
• He was, I believe, the greatest communicator
of maths.
“I go up to calculus, and beyond that I don’t understand
any of the papers that are being written. I consider that
that was an advantage for the type of column I was doing
because I had to understand what I was writing about,
and that enabled me to write in such a way that an
average reader could understand what I was writing
abut. If you are wiritng popularly about math, I think it’s
good not to know too much math.”
Marin Gardner, 2004
Activity for KS3/4
Area dissection – links to Fibonacci
5
8
5
5 8
8
13
13
• Draw this square on squared paper
• Cut it up into 4 pieces along the lines
• Assemble the pieces into a rectangle
• What is the area of the square?
• What is the area of the rectangle?
• Explain
• Try with a different ‘Fibonacci triple’
• Can extend into ideas of
convergence and limits
Activity for KS3/4
Binary mind reading
• It’s a travesty that roman numerals are in the
mathematics NC but binary isn’t!
• This ‘trick’ fascinates students (it fascinated me)
• To explain it, ask students to draw up a table
with 2s, 4s, 8s, 16s and 32s columns and rows
for each number from 1 to 63, to enable them to
translate the numbers 1 – 63 into binary (great
revision of place value ideas that can really
help them to understand base 10, as well as
revealing the awesome power of binary)
Activity for KS3/4
Binary mind reading
• They can then use their table to make up their
own cards and try the trick out themselves
32 16 8 4 2 1
1 0 0 0 0 0 1
2 0 0 0 0 1 0
3 0 0 0 0 1 1
Etc. Etc. Etc. Etc. Etc. Etc. Etc.
61 1 0 1 1 0 1
62 1 1 1 1 1 0
63 1 1 1 1 1 1
Activity for KS3/4
Cyclic number
• The basis of the trick is that, as decimals,
sevenths are cyclic numbers
• Reciprocals of some other primes are also
cyclic – it’s worth Googling!
. . . . . .
. . . . . .
1 2 30.142857, 0.285714, 0.428571
7 7 7
4 5 60.571428, 0.714285, 0.857142
7 7 7
Activity for A level
Folding surprise
• Take a circle of paper
• Mark a point on it, not at the centre
• Fold the circle so that the perimeter of the
circle touches that point, then unfold to leave a
fold line
• Repeat many times, folding different points on
the perimeter to touch the point inside the
circle, building up an envelope of fold lines
Folding surprise
• What shape is the envelope of folds?
• Can you prove it?
Activity for A level
Interesting problems/puzzles
• Martin Gardner published many interesting
puzzles and problems
• These are 4 of my favourites
1. Guess the diagonal
5 5 D C
B A
How long is AC?
Interesting problems/puzzles
2. The repetitious number:
• Write down a 3 digit number.
• Repeat the digits to produce a 6 digit number.
• Divide it by 7 (don’t worry, they won’t be a remainder).
• Divide the result by 11 (no remainder again).
• Divide by 13.
• You have back your original number. Why?
Great for KS3, really understanding place value and
factorisation.
Interesting problems/puzzles
3. The early commuter: A commuter always arrives at his
local station at exactly 5pm, and his wife always arrives
at exactly 5pm to drive him home from the station,
always taking the same route. One day he is able to
leave work early and catches the train that will get him
home at 4pm instead. It’s a nice day, so rather than
letting his wife know, he decides to walk home on the
route she drives, so she can pick him up when they
meet. His plan works perfectly and he gets home 10
minutes earlier than usual. Assuming she always drives
at a constant speed and that she left just in time to meet
his normal train, for how long was he walking before
she picked him up?
Interesting problems/puzzles
4. Hole in the sphere
‘This is incredible problem – incredible because
it seems to lack sufficient data for a solution. A
cylindrical hole six inches long has been drilled
straight through the centre of a solid sphere.
What is the volume remaining in the sphere?’
We glibly talk of nature’s laws
But do things have a natural cause?
Black earth turned into yellow crocus
Is undiluted hocus pocus.
Piet Hein [Quoted at the start of Martin Gardiner’s autobiography,
entitled ‘Undiluted Hocus-Pocus’]
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