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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 3m
Yes. In my early morning musings this morning, as part of my daily panic "What am I going to tweet today?" I stumbled on this (new?) way to construct doubly-fractal sequences. Should indeed make a video about them!
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James Tanton 2h
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James Tanton 2h
In 1,1,2,1,2,3,1,2,3,4,1,2,3,4,5,1,.. integer n first appears in nth triangular nmbr position. Delete those first appearances and what remain is the original sequence! Create a sequence so that each integer n first appears in position n^2 & deleting those entries gives orig seq.
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James Tanton 12h
. Yesterday a day of rest. Today S=7,R=40,T=280.
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James Tanton 24h
3 facts/5 mathers.1)Appeared on "Wheel of Fortune" (Aussie version) when 18. Had never watched the show! 2) I make a top-notch no-bake cheesecake (& pav!) 3)Not athletic, but been on top of highest peak of 2 continents.
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James Tanton Aug 22
A sequence has the property that for each prime number p, the p-th, 2p-th, 3p-th, 4p-th, ... entries, as a sequence in their own right, is identical to the original sequence. Must the original sequence be constant?
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James Tanton Aug 21
Yes. Canadese is the way! I was going to make such a point too. It's actually much more natural to speak in terms of "half a turn" and "one sixth of a turn" and the like. In fact, this is exactly what I do in this PENCIL PUSHING experience:
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James Tanton Aug 21
Out of curiousity (or is it my ego?) might it be the childhood bedroom-ceiling path-walking puzzle to which you refer? (My fave!)
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James Tanton Aug 21
1 radian<-->r units of arclength; 2 radians<-->2r units of arclength; x radians<-->xr units of arclength. So we have the formula arclength L = xr where x is count of radians. Now ,physically, L is a length, r is a length, which means x cannot be. Radians must be dimensionless.
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James Tanton retweeted
Tarquin Publications Aug 21
That was a rogue - current stock all has titles! And improved paper too. MoMath in NYC have copies right now also.
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James Tanton Aug 21
So now the issue is ... what to do about the natural misconception that could follow, that a radian is a measure of length? Subtle! In scaled circles one radian is the same amount of turning for all, but the lengths along arcs are not same. This is a challenging nuance!
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James Tanton Aug 21
They're from but are most readily available in the US via amazon, say. But I don't know now if you should enter a title when searching : ). Does leaving the title section blank now bring them up??
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James Tanton Aug 21
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James Tanton Aug 21
I actually think we should do radians really early on, giving the story that "360" is a very natural number for us Earthlings, but not for the math. Radians are not at all mysterious - but we make it that way!
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James Tanton Aug 21
We train Ss to work & think "degrees" for ten years straight, and then suddenly change to radians in pre-calculus for no apparent need. The need only comes later for when you differentiate sin(x), say. You see degrees are unnatural to the math. So do radians then. (Or..do early.)
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James Tanton Aug 21
1,1,2,1,4,2,8,1,16,4,32,2,64,8,.. has the property that pulling out every 2nd term gives a copy of original sequence: 1,1,2,1,4,2,8,.. Is there a (non-const) sequence with the property that pulling out every 2nd term or pulling out every 3rd term each give a copy of the original?
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James Tanton Aug 20
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James Tanton Aug 20
. has had a tremendous number of requests to create a prof. development certification program on . We've just created one in partnership with Edfinity! . Warning:There is a (nominal, truly nominal) fee for this optional service.
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James Tanton Aug 20
Oh dear! The pressure is on! Okay .. I promise to be amazing. (But do know I am going to be boring in one respect: The International Math Salute is going to happen! )
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James Tanton Aug 20
This is yet another thoughtful and profound piece from the esteemed , but did you catch that he and are going to be in NY on November 5th?!!! My New York colleagues ... be there!
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