560 reputation
211
bio website economicdroplets.com
location London, United Kingdom
age 61
visits member for 2 years, 8 months
seen Jul 11 at 20:34

Professionally I am interested in finance and economics, and in maths and statistics relevant to those areas. I have degrees in economics, philosophy and business administration, and have recently completed an MSc in Applied Environmental Economics. I am also a qualified accountant (ACMA / CGMA).

As a hobby, I am also interested in number theory and geometry.

My website is a blog on environmental and natural resource economics.


Jun
25
answered Fermat's Last Theorem near misses?
Jun
11
answered What is an example of real application of cubic equations?
Jun
11
comment What is an example of real application of cubic equations?
For similar reasons the maximum power that can be generated by a wind turbine is proportional to the cube of the wind speed.
Jun
6
comment A question about squares
It may be significant that the number of remaining rows in 2013 x 2013 equals (2013 - 1)/4 = 503. That may give a clue to a closed form formula for the number of remaining rows in n x n.
Jun
6
comment A question about squares
A simple example is n = 3 (zero cells remaining since 1 is in row 1, 4 in row 2 and 9 in row 3, one quadratic non-residue (2)). n = 2013 is also an example, since there will be many rows not deleted in the lower regions of the square, the intervals between the larger squares being greater than the length of a row.
Jun
6
comment A question about squares
A proposition that is true for any n x n is that if you delete only the columns containing a square, the number of remaining columns will equal the number of quadratic non-residues. If you also delete rows containing a square and count the remaining cells, the number will equal the number of quadratic non-residues only if all rows except one are deleted. This happens to be so for some cases with small numbers, eg 4x4 and 5x5, but is not true in general.
May
17
comment Positive integer solutions of $a^3 + b^3 = c$
@BrianJ.Fink The modular constraints are best thought of not as flagging possible solutions but as excluding impossible values, either impossible values of $c$ or, for given $c$, impossible values of $a^3,b^3$. The exclusion of values which are impossible for modular reasons from the set of all positive values of $c,a^3,b^3$ can help to find positive solutions faster. It doesn't matter if, as is the case, the modular constraints also apply to $a^3+(-b)^3=c$.
May
16
comment Positive integer solutions of $a^3 + b^3 = c$
There are also modular constraints which don't exclude values of $c$ but lead to modular conditions on any associated $a^3$ and $b^3$. For example, if $c \equiv 2\mod 7$ then $a^3,b^3 \equiv 1\mod 7$.
Dec
31
awarded  Yearling
Dec
13
revised Identifying Ways of Dividing an Area into Merged Regions
Update with new idea for solution
Dec
12
awarded  Organizer
Dec
12
revised Are the following definitions of a uniform continuous variable equivalent?
Add appropriate tag (previously untagged).
Dec
12
suggested suggested edit on Are the following definitions of a uniform continuous variable equivalent?
Dec
11
answered Are the following definitions of a uniform continuous variable equivalent?
Oct
23
comment Identifying Ways of Dividing an Area into Merged Regions
Please ignore the last sentence of my earlier comment which is confused (wasn't quick enough to edit it). A further thought: will this method identify all possible divisions? Some divisions will need more than one move from the starting division and I can't see that the method as stated allows for that.
Oct
23
comment Identifying Ways of Dividing an Area into Merged Regions
Thank you, an interesting suggestion. At step 3, presumably $r$ would be chosen from those derived regions that had not already been obtained by moving an original region at step 2?
Oct
22
revised Identifying Ways of Dividing an Area into Merged Regions
Improve consistency of terminology.
Oct
21
asked Identifying Ways of Dividing an Area into Merged Regions
Oct
13
comment How many solutions to $x^3+y^3 = z^3\pm 1$ for $z$ less than a bound?
A key difference between (1) and (2) is that in (2) the number of terms on the left is one less than the power. For sufficiently large N I would expect $\Delta N$ for (2) to approximate to $kH_N$ where k is a constant and $H_N$ is the Nth harmonic number. If so the limit of $\Delta N/N$ will be zero.
Sep
17
comment Does this Diophantine cubic have solutions?
Please see the following similar question which has some relevant answers: math.stackexchange.com/questions/61014/solve-x3-1-2y3/…