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IntMath Newsletter: Tesla multiplication map, resources

By Murray Bourne, 26 Jul 2016

26 Jul 2016

In this Newsletter:

1. Tesla Map to Multiplication
2. Resource: Better Explained
3. Math in the news: China's own Good Will Hunting
4. Math technology history - pinwheel mechanical calculator
5. Math puzzles
6. Final thought: Universal passport?

1. Tesla Map to Multiplication

(a) 3D animation of Tesla's Map to Multiplication

Tesla multiplication applet

I recently came across an interesting Map to Multiplication, reported to be by inventor Nikola Tesla, which shows interesting patterns between products of numbers. I created a 3D animation to demonstrate what it's all about:

3D animaion of Tesla's Map to Multiplication

(b) The real story behind the Tesla Map to Multiplication

Story behind the Tesla multiplication applet

The fascinating Map to Multiplication may not be all it seems, notwithstanding its cleverness.

The real story behind the Tesla Map to Multiplication chart

2. Resource: Better Explained

Better Explained covers a wide range of math topics using intuitive and easy-to-follow methods, in some cases with interactive activities. Here are some example pages:

3. Math in the news: China's own Good Will Hunting?

China's own Good Will Hunting?

In the CNN article, China's 'Good Will Hunting?' Migrant worker solves complex math problem, we read about a parcel delivery man with no formal higher math education who has developed an alternative method to verify Carmichael Numbers.

(A Carmichael number appears to be a prime, based on Fermat's Little Theorem, but turns out to be composite. The first Carnichael number is 561.)

The story is reminiscent of S. Ramanujan's rise to academic prominence with no formal background, and of the movie Good Will Hunting.

4. Math technology history - pinwheel mechanical calculator

Brunsviga Pinwheel Mechanical Calculator
Brunsviga Pinwheel Mechanical Calculator
German, circa 1895

I came across this 120 year-old calculator in a museum in Cambridge last year. Here's what the caption said:

This machine can mechanically calculate sums using a complex system of pinwheels coupled with geared carry mechanisms and a counter. Users would input numbers and
turn the handle clockwise for addition and multiplication or counter-clockwise for subtraction and division.

Although the principle of such an arithmetic machine was described by Gottfried Leibniz in 1685, it was only in 1873 that there was a practical, affordable design suitable for mass production.

The owner of this particular device was George Udny Yule, appointed Cambridge's first University Lecturer in statistics in 1912.

5. Math puzzles

The puzzle in the last IntMath Newsletter (28 Jun) involved buying a combination of plants.

Correct answers with sufficient explanation (which included reasoning) were given by: Γιώργος, Kai, Nour, Lidia, Don, Rasheed, Helena and Chris.

Some of the solutions included the trivial case of buying 100 yams, but the wording of the question ("I grab a selection of plants...", and "How many of each type ...") suggest the trivial answer shouldn't be included.

It's unfortunate that most school mathematics questions have one clear correct answer, usually arranged that way so it's easier to grade and there is less controversy about fairness. But in the real world, most problems are "fuzzy" and multi-variable, often with several ways to do it and several outcomes. Students should get more experience with such open-ended problems. I think it's good to mention the trivial case as one possible outcome, but I don't think we would include it as a solution in this case.

New math puzzle

The 1st of January 1981 was a Thursday. What day of the week was the first day of the 20th century?

You can leave your responses here.

6. Final thought: Universal passport?

Inequality of wealth distribution is no doubt a big part of recent unfortunate events (in the eyes of many) like Brexit, the shift to the right in Europe and the rise of Donald Trump. Here's a perspective that's worth pondering:

Money is an article which may be used as a universal passport to everywhere except heaven, and as a universal provider for everything except happiness. [Wall Street Journal]

Until next time, enjoy whatever you learn.

See the 14 Comments below.

14 Comments on “IntMath Newsletter: Tesla multiplication map, resources”

  1. Blessing says:

    1 January 1981 = Thursday
    1 January 2000 = ?

    => 2000-1981 = 19
    :.1 Jan 2000 = Thur + 19 days(01/011981 = Mon,01/01/1982 = Tue)
    = 19 -: 7 (7 DAYS IN A WEEK)
    = Thur + 5 days
    = Tuesday

    That's what think

  2. Sigmund Krieger says:

    The interval between 1/01/1981 and 1/01/2000 was 6,939 days; or 1/01/2000 was a Saturday.

  3. Nour Hlwani says:

    "First day of 20th century" = 1 january 1901

    And according to my calendar 😛 :
    1/1/1901 is a "Tuesday".

  4. Soorya Kant Mandaldutta Ojha says:

    Monday: Every general year adds 1 DAY, every leap year adds 2 DAYS, so 20 years = 5 leap years + 15 general years = 5*2+15*1=25 DAYS, divided by 7 gives 21+4, i. e. 4 DAYS ahead= Monday.

  5. Γιώργος Βαρελάς says:


    The first day of the 20th century is 01/01/1901 rather than 1/1/1900.
    I was born on June 4, 1957, Tuesday. Every 28 years (but after 1900 was not a leap year) always coincide the same day (every four years is a leap year and the week's been seven days: 4x7 = 28), even for those who were born February 29th. Indeed, 01/01/1957 was this Tuesday (31-1 + 28 + 31 + 30 + 31 + 4 = 154 = 7x22). Since then 1957-1901 = 56 = 2x28, then the day 01/01/1901 was Tuesday.

  6. joshua says:

    It was a Sunday. Continue to produce this paper it is good to us mathematicians

  7. Don Miller says:

    The number of days between Jan 1 1900 And Jan 1 1981 is

    DAYS=((81-1)/4)*366 +(81-1)*3/4)*365 =29200

    29200MOD(7) = 3

    Now, go back 3 days from Thur.......Monday

    Ans = Monday

    Note 29200/7 =4171 + 3 I.e. 29200 MOD(7)

  8. RaySF says:

    Hi Murray
    and thanks^million for the wonderful Newletters and inspiration!

    In the "Comment permalinks" (in Puzzle Answers, etc), do include a "short link" of the permalink instead of the long URL.

    So for ex.,the loooong "Comment permalink":

    becomes, simply:

    Much easier to save many bookmark permalinks to Puzzle answers and other interesting intMATH blog content, for future reference... 🙂


  9. Murray says:

    @Ray: Thanks for the kind comments.

    Actually, I did have a URL shortening system on IntMath for a year or so, but it messed up search results and I had to abandon it.

    I'm not sure where you are saving your bookmarks to, but if it is to MS Word for example, rather than save the long URL, why not save the full link, like this (this comes from the "See the 17 Comments below" bit at the end of the post):


    Then change that text to something short and meaningful:

    Solutions for plants puzzle

  10. Colin Morrison says:

    First day of the 20th century was 1 January 1901, a Tuesday.

  11. Mawazo says:

    1St Jan 1900 was a Monday

  12. Ben Murray says:

    The answer here depends if we consider the 1st day of the 20th C to be 01/01/1900, or 01/01/1901. I'm a purist, so I go for the latter 🙂

    So 01/01/1981 minus 01/01/1901 equals 80 years.

    60 of these are ordinary years of 365 days, for a total of 21900 days

    20 of them are leap years of 366 days, for a total of 7320.

    Overall total is 29220 days.

    29220 Mod 7 = 2, i.e. if we divide 29220 by 7 there are 2 left over.

    Two days back from Thursday is Tuesday, which is the what the 1st of Jan 1901 was.

    If we want to go back to the 01/01/1900 for the sake of argument, we need to add on an extra 365 days to our total (1900 wasn't a leap year in the Gregorian calendar). So the total number of days is 29585.

    29585 Mod 7 = 3, so we need to go back three days from Thursday, making 01/01/1900 a Monday.

  13. Rick says:

    Days of the week also depend on when countries adopted the Gregorian calendar. Greece, Russia and 6 or 7 other countries with names ending with "ia" were using the Julian calendar on 1-1-1901. To them, the day of the week would have been a Monday.

    Test your day of the week algorithm for 9-13-1752.

  14. Murray says:

    @Rick: Very good point! We all assume *our* calendar is what everyone else uses. It's amazing how long the Julian calendar, with all its inaccuracies, lasted. We'll be saying the same thing about the British units of weights and measures sometime...

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