Jason Dyer
  • Member for 12 years, 3 months
  • Last seen more than 5 years ago
Proofs without words
193 votes

The cardinality of the real number line is the same as a finite open interval of the real number line.

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Most harmful heuristic?
81 votes

Linear algebra purely as row manipulations. I've written about this here: Students stuck in a rut of thinking of matrices as a clever way to arrange numbers will get lost and confused; I know ...

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Alternatives to pi day
29 votes

Paradox Day, which happens on a random day during the year such that it is unexpected which day it is, except of course it couldn't happen December 31st because we'd know by December 30th that it'd ...

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effective teaching
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24 votes

The topic you touch upon is vast, but I wanted to comment on this phrase: "problem/solution patterns which is very different from showing them the underlying conceptual tapestry". If for ...

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If you break a stick at two points chosen uniformly, the probability the three resulting sticks form a triangle is 1/4. Is there a nice proof of this?
21 votes

Is the argument you remember along the lines of: picking three points on a circle, what is the probability they lie in the same semicircle? The problem is discussed here: http://godplaysdice....

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How to teach addition of negative numbers?
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15 votes

It would help to know a little more about the nature of your friend's dyscalclia. The sense of the integer line comes from the inferior parietal cortex (and causes difficulty with problems like "what ...

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What is the term analogous to "Wronskian" for difference equations?
Accepted answer
14 votes

You mean "Casoratian"?

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Why the search for ever larger primes?
14 votes

There was a significant real-life effect to the effort to discover primes: it was how the infamous Pentium bug was discovered. Professor Thomas Nicely, then a professor of mathematics at ...

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A problem of an infinite number of balls and an urn
11 votes

The second part is the paradox of Thomson's lamp, which can be formalized as thinking about Grandi's series $\sum_{n=0}^{\infty}{(-1)^n}$. This is a decent summary; one can argue either "the sum ...

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Twin Prime Conjecture Reference
11 votes

Euclid never made a conjecture about the infinitude of twin primes. It is possible to guess that he was making a conjecture on the basis of his text but it requires wishful thinking. Here is the ...

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Are there elementary-school curricula that capture the joy of mathematics?
11 votes

As far as a full curriculum goes, I don't believe there is one that does exactly what you want. Books (in the United States, at least) divide into two camps: "Constructivist" (e.g. Everyday Math, ...

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Where can I find the text of Weyl's Fields Medal speech for Serre?
9 votes

Is this sufficient? http://www.springerlink.com/content/23260u245q251055/

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Earliest diagonal proof of the uncountability of the reals.
8 votes

From Labyrinth of thought: a history of set theory and its role in modern mathematics by José Ferreirós and José Ferreirós Domínguez: page 184 (quoting a margin note of Cantor's) Besides, ...

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What practical applications does set theory have?
7 votes

While I'm unsure any straight uses of set theory, fuzzy set theory gets used directly in quite a few areas (engineering, medicine, business, social sciences) where information is incomplete. See for ...

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Pronunciation: Crapo
7 votes

KRAY-poe. The name is of French origin.

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Must a locally compact group be Hausdorff in order to possess a Haar measure?
Accepted answer
6 votes

No. Simon Rubinstein-Salzedo's "On the existence and uniqueness of invariant measures on locally-compact groups" presents a proof of existence (and uniqueness up to a multiplicative strictly positive ...

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Name of the Marshall Hall paper in which he proved that the intersection of all subgroups of a fixed finite index is again finite index?
6 votes

Subgroups of finite index in free groups. Canadian J.Math., 1:187–190, 1949.

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Just starting with [combinatorial] game theory
6 votes

In addition to Winning Ways for your Mathematical Plays, I also recommend the books Games of No Chance and More Games of No Chance. Many of the articles from Games of No Chance are online.

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Fundamental Examples
6 votes

Tic-Tac-Toe tends to be the starting example in combinatorial game theory, just because it's simple enough to depict the entire tree on one page yet can still be used to illustrate the standard ...

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Special cases for efficient enumeration of Hamiltonian paths on grid graphs?
Accepted answer
5 votes

There are certainly special graphs that are always Hamiltonian (if every vertex of a graph of n vertices has degree at least n/2, say) and these have efficient algorithms associated with them. For ...

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How Does Random Noise Typically Look?
4 votes

I am still thinking about the original problem, but let me discuss the side problem of random strings. In the infinite case the proper way to designate "random" is fairly similar to the "random tree" ...

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Is there a theorem that says that there is always more than one way to "continue a finite sequence"?
4 votes

I believe you mean "describable by a polynomial formula", in which case the answer is "yes". Given $n$ terms $s_0, \cdots, s_{n-1}$, start with a polynomial of degree $n$: $$a_1x^n+a_2x^{n-1}+ \...

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Graphs with fractal properties?
4 votes

You could start with graphs directly based on fractals, like the Sierpinksi Graph or the Koch Graph. For future searching, these are called "self-similar graphs".

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Godel's 1st incompleteness theorem - clarification.
4 votes

As already pointed out here by Tom Leinster, "true" doesn't make sense without some sort of model. It is a technical word.

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Variation on a matrix game
3 votes

While I still can't answer in the general case, in the case where n > 2 and Alan moves only with 0 in attempt to fill a row or column with 0s, he cannot win. This proof is written semi-informally ...

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Why do branches of math vary in proof styles and what category are different branches in?
3 votes

This reminds me of Terry Tao's essay contrasting hard analysis and soft analysis: At first glance, the two types of analysis look very different; they deal with different types of objects, ...

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Dance battles and de Bruijn sequences
3 votes

Your original answer would have been correct had the dancers had been simply searching for an optimal path through the movements to traverse as much of the graph as possible. You need to account for ...

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Is there a combinatorial interpretation of the identity $\sum_{k=0}^m 2^{-2k} \binom{2k}{k} \binom{2m-k}{m} =4^{-m} \binom{4m+1}{2m}$?
2 votes

Since you describe yourself as a "layman" I'm guessing you don't want to hear about the Haar measure on Grassmannian space G(n,1), so here's my best intuitive explanation of the left hand side of the ...

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Upper bound on the area of a midpoint pentagon?
2 votes

It's called a "midpoint polygon". The problem seems to be addressed (with proofs for triangles and quadrilaterals but only a conjecture for the pentagon) here: http://techhouse.brown.edu/~mdp/...

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What is induction up to epsilon_0?
1 votes

David, if you are still confused, note that any ordinal under $\epsilon_0$ can be converted into what is essentially a base-ω positional numeral system. There are more details here.

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