In 1975 John Fahey released an LP including the track “The Assassination of Stefan Grossman”:
Stefan Grossman responded in the only way possible, with the assassination of John Fahey:
Why John Fahey chose to assassinate Stefan Grossman in the first place, nobody knows, not even Stefan Grossman.
Following the discovery of a question to which the answer is 42, the same team has now reported a sum of three cubes equal to 3. As before, the result can be checked from Excel, linking to mpmath, via pyxll.
In the first example each of the three cubes is evaluated, and the resulting strings are concatenated into a single string function that is evaluated:
The mp-Eval function also allows values to be assigned to symbols, which can then be evaluated. In this example the letters a to d are replaced with the values in the cells to the right, and substituted into the function in cell A41:
Using the same approach, a rather simpler solution to the problem can be found:
Further discussion of the background to this problem can be found at The Math Less Travelled, which has links to on-line calculators to solve the problem summing to 42, and it is also pointed out that that the formula can be evaluated directly in Python:
Also worth a read is the Wikipedia article on the sum of three cubes, which contains further examples and numerous links.
Posted in Computing - general, Excel, Link to Python, Maths, Newton, PyXLL
Tagged 42, Excel, Life the Universe and Everything, mpmath, PyXLL, sum of 3 cubes
Yesterday the sound on my HP Omen computer stopped working for no apparent reason. I found the video below, which fixed the problem:
The video is short, easy to follow, and doesn’t need the sound working to understand it!
The procedure on my machine was pretty much as shown in the video except:
- The Device Manager was not listed when I clicked on the Windows Icon. Just start typing “Device Manager” and it appears.
- The Sound driver listed for my machine was “Realtek(R) Audio”
- I had to restart the computer after re-installing the driver.
A recent question at Quora asked: “Why am I getting an overflow error in Excel VBA when doing a simple arithmetic calculation like str1 = 24*60*30 where str1 is a variant or long or double?”
I hadn’t encountered that problem before, but a quick check confirmed that it does raise an error, whatever the data type of str1 (including Integer).
There is a detailed answer to this question at:
In short, the problem is that the result data type defaults to the largest type of the values being operated on, so if they are all integers the result is an integer, and since the largest value for an integer is 32767 you get an overflow.
Alternatives ways to avoid the problem include:
- Add a decimal point to at least one number, converting it to a double.
- Convert at least one value to a Long: str1 = CLng(24) * 60 * 30
- Declare at least one value as a Long constant:
Const HrPerDay As Long = 24
str1 = HrPerDay * 60 * 30
The variable used to receive the result of the calculation must of course also be at least a Long, since a value greater than 32767 cannot be assigned to an integer.
It might be expected that a similar problem would arise if one value was converted to a double, so that the result of the calculation was a double, and this was assigned to a Long, but in this case the data type is automatically converted by VBA to suit the variable receiving the value.
Recent versions of Windows have provided indexing of file contents that allows for fast searches over the entire contents of your hard disk. This includes pdf files, but the default filter file only works with 32 bit Windows. It is simple process to fix this problem by downloading an updated filter file. for full details see:
The indexing process takes time, but once completed it is updated in the background with no noticeable effect on performance.
Once indexing is complete, the Windows File Explorer provides very fast searches of all indexed folders, and fast preview of selected files:
is 42, as is well-known:
The actual question, to which the answer is 42, is not known, but a lesser known long standing question involving this number has recently been solved:
The original problem, set in 1954 at the University of Cambridge, looked for Solutions of the Diophantine Equation x^3+y^3+z^3=k, with k being all the numbers from one to 100. 42 was the last remaining number (for which a solution is possible), but recently a solution was found by a team led by the University of Bristol and Massachusetts Institute of Technology. The answer is:
(-80538738812075974)^3 + 80435758145817515^3 + 12602123297335631^3
If we try to check this result in Excel we find that the available 15 significant figure accuracy is not quite up to the job:
But calling the mpmath package, via pyxll, finds that the solution is indeed correct:
There are many sites discussing the Mandelbrot Set, but not many examples using VBA to plot the set in Excel, so here is my effort:
The spreadsheet (including open source VBA code) may be downloaded from:
Note that to keep the download file a reasonable size the file has been saved with a low resolution image. 350 x 350 resolution gives a good compromise between image quality and speed of processing and plotting.
Required input is:
- Centre point coordinates
- Plot width (= height)
- Plot resolution
- Number of iterations
The results are plotted as a scatter chart with 7 data ranges, plotting markers only.
The plot below was generated with 28 iterations, and a resolution of 350×350. Calculation time was 0.33 seconds:
The second example was taken from:
How To Quickly Compute The Mandelbrot Set In Python
Higher resolution (1000×1000) with 2048 iterations resulted in much longer calculation time, but times are 2-3 times faster than the plain Python code given in the link:
For faster plotting compiled code is required. A good site providing fast high resolution plots for user selected location, scale and number of iterations is:
The site text says the plots will not work in Microsoft browsers, but they worked with no problem for me in Internet Explorer. The image below was generated in the spreadsheet using parameters from the link above.
Posted in Charts, Charts, Coordinate Geometry, Drawing, Excel, Maths, Newton, VBA
Tagged Charts, Excel, Mandelbrot Set, VBA