query | a pythonic query language |
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R(n@1) | R(r@1) | R(b@1) |
---|---|---|
7 | 4 | 2 |
9 | 7 | 2 |
25 | 21 | 2 |
27 | 19 | 2 |
81 | 55 | 2 |
121 | 111 | 2 |
125 | 101 | 2 |
169 | 157 | 2 |
243 | 163 | 2 |
361 | 343 | 2 |
625 | 501 | 2 |
729 | 487 | 2 |
841 | 813 | 2 |
4 | 3 | 3 |
25 | 21 | 3 |
49 | 43 | 3 |
125 | 101 | 3 |
289 | 273 | 3 |
343 | 295 | 3 |
361 | 343 | 3 |
625 | 501 | 3 |
841 | 813 | 3 |
961 | 931 | 3 |
3 | 2 | 4 |
5 | 3 | 4 |
7 | 4 | 4 |
9 | 7 | 5 |
27 | 19 | 5 |
49 | 43 | 5 |
81 | 55 | 5 |
243 | 163 | 5 |
289 | 273 | 5 |
343 | 295 | 5 |
529 | 507 | 5 |
729 | 487 | 5 |
121 | 111 | 6 |
169 | 157 | 6 |
289 | 273 | 6 |
3 | 2 | 7 |
4 | 3 | 7 |
121 | 111 | 7 |
169 | 157 | 7 |
289 | 273 | 7 |
529 | 507 | 7 |
6 | 4 | 8 |
25 | 21 | 8 |
121 | 111 | 8 |
125 | 101 | 8 |
625 | 501 | 8 |
841 | 813 | 8 |
5 | 3 | 9 |
7 | 4 | 9 |
Parameters:
b, n, r
Both fields and conditions are made up of terms.
A term is a valid Python expression in a name space made up of:
database parameters;
any imported python modules;
PyQL Aggregators such as Average (A), Sum (S), and Replace (R);
and other domain specific terms.
About the Barely Rational Database | Sample Queries |
---|---|
n are integers from 2 to 1001.
r is the number of 'digits' required to represent 1/n (+1 for the bar). b is the base. Primes is a list of prime numbers. |
To see n vs r in base 10, use the PyQL: n,r@b=10
To see n vs r in base 10 graphically, use the PyQL:
To see n vs r for bases 2 - 10, use the PyQL:
To see n vs r for bases 2 - 10 for prime n, use the PyQL:
To see n vs r for bases 2 - 10 with icons colored by primeness, use the PyQL:
To see n v r/n for bases 2 - 10 with icons colored by primeness, use the PyQL:
To see n v r/n with icons colored by primeness for bases that are perfect squares, use the PyQL:
n v math.log(r/n) seems to have something to tell us:
What about those dots between the main lines in these graphics? Are there patterns to those barely rational numbers?
Let's have a peek with a histogram:
We can have a closer look with that most excellent data visualization tool called a table of numbers:
Another nice query is:
Let's continue to graphically explore the cases of non-integer n/r. To start, let's look at n/r between 1 and 2 with the PyQL:
There is a lot going on there and and coloring by oddness reveals a pattern:
Grouping by n being a perfect square shows in interesting set of numbers. |