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If I measure the diagonal distance of a unit square I have a distance of 1.4, if instead I use the Taxicab distance, then the distance is 2. Now suppose I make the lines segments of the taxicab zigzag smaller and smaller - at some point they will look just like a diagonal.
I assume that even as the segments approach zero length they will still always add up to 2, yet my feeling is that they "should" eventually be indistinguishable from the diagonal they look like with a distance of 1.4.
So what am I missing, why doesn't the length approach 1.4 as the segments get smaller? Ariel. ( talk) 02:49, 7 May 2017 (UTC)
Hi,
Suppose we have a directed graph, where the in-degree of each vertex is , and also, the out-degree of each vertex is . Now, each vertex is colored in one of the colors (uniformly and independently). For each vertex we denote to be the event that don't have an out neighbor with the same color as .
My question is: Given a vertex , what is (at most) the size of the group ?
Thanks in advance — Preceding
unsigned comment added by
31.168.108.114 (
talk)
10:10, 7 May 2017 (UTC)
We know that the worst case for trial division is when n=p^2. Therefore p=sqrt(n). Assuming the worst case and naïve trial division(all integers), the time is only sqrt(n), and therefore is sub-linear. So why is factorization so hard? 32ieww ( talk) 16:26, 7 May 2017 (UTC)
Is it true that all the numbers in a prime-numbered row of Pascal's triangle are divisible by said prime number except for the 1s at the ends? 32ieww ( talk) 16:35, 7 May 2017 (UTC)
We know there are 11 kinds of polyforms in 2 dimensions (plus their topological equivalents.) They are:
Any web sites that reveal names of these 2 kinds of polyforms?? MathWorld doesn't. Georgia guy ( talk) 17:54, 7 May 2017 (UTC)
Mathematics desk | ||
---|---|---|
< May 6 | << Apr | May | Jun >> | Current desk > |
Welcome to the Wikipedia Mathematics Reference Desk Archives |
---|
The page you are currently viewing is an archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages. |
If I measure the diagonal distance of a unit square I have a distance of 1.4, if instead I use the Taxicab distance, then the distance is 2. Now suppose I make the lines segments of the taxicab zigzag smaller and smaller - at some point they will look just like a diagonal.
I assume that even as the segments approach zero length they will still always add up to 2, yet my feeling is that they "should" eventually be indistinguishable from the diagonal they look like with a distance of 1.4.
So what am I missing, why doesn't the length approach 1.4 as the segments get smaller? Ariel. ( talk) 02:49, 7 May 2017 (UTC)
Hi,
Suppose we have a directed graph, where the in-degree of each vertex is , and also, the out-degree of each vertex is . Now, each vertex is colored in one of the colors (uniformly and independently). For each vertex we denote to be the event that don't have an out neighbor with the same color as .
My question is: Given a vertex , what is (at most) the size of the group ?
Thanks in advance — Preceding
unsigned comment added by
31.168.108.114 (
talk)
10:10, 7 May 2017 (UTC)
We know that the worst case for trial division is when n=p^2. Therefore p=sqrt(n). Assuming the worst case and naïve trial division(all integers), the time is only sqrt(n), and therefore is sub-linear. So why is factorization so hard? 32ieww ( talk) 16:26, 7 May 2017 (UTC)
Is it true that all the numbers in a prime-numbered row of Pascal's triangle are divisible by said prime number except for the 1s at the ends? 32ieww ( talk) 16:35, 7 May 2017 (UTC)
We know there are 11 kinds of polyforms in 2 dimensions (plus their topological equivalents.) They are:
Any web sites that reveal names of these 2 kinds of polyforms?? MathWorld doesn't. Georgia guy ( talk) 17:54, 7 May 2017 (UTC)