Math Is Fun Forum
Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °
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#1 2010-03-19 23:45:06
- JaneFairfax
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- Registered: 2007-02-23
- Posts: 6,868
Cute little problem I saw on another site
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#2 2010-03-20 00:00:19
- mathsyperson
- Moderator
- Registered: 2005-06-22
- Posts: 4,900
Re: Cute little problem I saw on another site
Ah, now I see how this works. Nice puzzle.
Why did the vector cross the road?
It wanted to be normal.
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#3 2010-03-22 18:37:04
- scientia
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- Registered: 2009-11-13
- Posts: 224
Re: Cute little problem I saw on another site
In general, for , we have
This can be proved by induction. For the inductive step, note that
Hence, for this problem,
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#4 2010-05-06 07:54:09
- JaneFairfax
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- Registered: 2007-02-23
- Posts: 6,868
Re: Cute little problem I saw on another site
scientia wrote:
In general, for , we have
This is a very neat formula. It also proves that if
then −1 ∊ M[sub]n[/sub]
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