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James Tanton
An Aussie fellow promoting uplifting joyful genuine math thinking and doing for students & teachers alike. Honored: reaching millions!
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James Tanton Feb 16
Replying to @republicofmath
Yep. Helping with a family issue here. (But clearly chiming in on Twitter every now and then.)
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James Tanton Feb 16
Of course, I meant to add “a>1” to make this question non-trivial. So, the very round numbers? Hmm.
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James Tanton Feb 16
A square hole cut from a square cake. The line through the 2 centers has the following 4 properties: cuts area of hole in half, perim of hole in half, A of cake in half, P of cake in half. For any shaped cake with matching shaped hole, must there be a line with all 4 properties?
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James Tanton Feb 15
Yep! Forgot to add a>1 (makes it more interesting!)
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James Tanton Feb 14
Which positive integers N cannot be written in the form N = a^2+b with a and b coprime (that is, gcf(a,b)=1)?
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Mike Lawler Feb 13
Replying to @dandersod @jamestanton
The paper cutting exercise reminds me a lot of a paper tearing exercise I saw from which is in the first video here (and I suppose the paper folding one in the 2nd video is a nice geometric series, too!):
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James Tanton Feb 13
Today’s Puzzzle: Impossible to write the number 17 as a sum a+b+c of positive integers with a,b,c each larger than 1 and gcd(a,b)=gcd(b,c)=gcd(a,c)=1. (Try it!) But can every number thereafter be so expressed? (I suspect this is something number theorists have already explored?)
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DrewƦ&ℝ Feb 13
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James Tanton Feb 11
The PUZZLE for the day after tomorrow: If we regard 1 as a prime number (blasphemy?) is it true that every positive integer is the sum of distinct primes? (eg 1=1, 2=2, 3=3, 4 =1+3, 5= 2+3, 6=1+5, 7=2+5, 8=3+5, 9=1+3+5, etc)
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James Tanton Feb 11
Perhaps we can view HS content not at all as "sacred content," content for its own sake, but instead its content pieces simply as vehicles for teaching thinking. Then doesn't matter what the content is -- except to say if it is not teaching thinking, then don't do it!
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James Tanton Feb 11
Off to Australia! Great stuff you are doing!
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James Tanton Feb 11
Heading abroad again so Twitter Puzzles will be spotty for a while. But here is something in my head: Tomorrow's PUZZLE today! Which even numbers N can be written as N=a+b, with a and b both odd numbers >1, sharing only 1 as a common factor (ie coprime)? eg 18=5+13, 100=27+73.
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James Tanton Feb 11
Irene .. et al. I would be happy to email you a PDF chapter on "circle-ometry" as I have done with students, in case you are interested. My old YouTube videos are old and a bit naive!
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James Tanton Feb 11
Just awesome! And visually lovely too. Gotta love them dots!
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Mrs. Cook Feb 11
Replying to @jamestanton
This was so fun!!! My algebra 2 student is taking on the challenge to develop his own polynomial ❤️❤️!🤓
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James Tanton Feb 11
Wow! What a stunning (100th!!) piece. Bringing mathematics home!
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James Tanton Feb 11
Inspired by FabMath participants: Within a 6x6 grid move top left to bottom right, talking only R and D steps. Start with 1 and add 1 with every R step (x -->x+1) and invert with every D step (x-->1/x). Which path(s) give smallest final value? (largest? Mean/median etc?)
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Sandi Berg Feb 11
Looking at the schedule for and so excited to know that , Renee Michaud and Terry Lakey will be there at the same time as I am!
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James Tanton Feb 10
It’s our Valentine’s brunch as I am going to be away next week. Such a lucky lucky fellow with L in my life. So much love.
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Sergio Belmonte Feb 10
we like that maths!
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