We will discuss a fast way to calculate logarithms on the Japanese abacus (soroban) up to the accuracy of 4 decimal places, without using logarithm tables. The method used here to produce an efficient algorithm for logarithm calculation can be applied to many other complicated functions.
Archive.org is a great website full of book rarities available for free download. The only problem is that most of their PDF files are quiet unreadable, not just on a tablet, but even on a stronger desktop PC, because they are optimized for minimal size, and it can take around 5-10 seconds for a tablet to render a page. This post shows a method for converting those PDF files to larger files (around 4x), which can be comfortably browsed offline even on a tablet.
CozyCL is a very simple, minimalist OpenCL library. You can run programs on your graphics card pretty easily with it, without the need to know anything about the data types of the base libraries (at least for the host program). When I started to learn about GPU programming in the previous weeks, I found even the most handy C++ bindings pretty time-consuming for a beginner, who is mostly interested in getting positive feedback and sense of achievement after a couple of initial attempts.
I’ve written the major part of this Buddhabrot rendering program in last August, and after a six months break I carried on with it again this weekend to close the project finally. But before going into details, let`s see what it does:
Few days ago I decided to create a C++ implementation of the Simplex algorithm, which is a tool for solving Linear Programming problems. One of my motivations could have been my recent encounter with the Eigen linear algebra library, which really surprised me with its beautiful syntax and easy usage. So I wanted to gain a little experience with Eigen, although some factorization-related project might have suited this purpose better. Another motivational factor was a not yet published project of mine, which might get finished in 1 or 2 months, and would give LP a real application.
This picture of the Moon is made from the average (mean) of 16 RAW images (14 bit), taken on the 30th of May 2012, around 23:30 (UTC+1), at Frankfurt am Main. I used my 9.25 inch Celestron telescope, with an adapter, which reduces its focal length, so the whole Moon fits in the screen, and also produces higher brightness level. The settings for the DSLR camera are: ISO: 100, Shutter speed: 1/400.
This post features two examples of algebraic manipulation and their relation to the symmetry of the matrices representing the expressions. The algebraic expressions we investigate are quadratic, multivariate and can be written in the matrix form:
While most diatonic chord progressions are based on the relations of the roots, some chromatic progressions can be thought as movements of voices. 1. If we have a minor triad in root position, and we move the 1st down and the 5th up by a semitone, then we get a minor triad in 6/3 position, and the root of the new chord is below the old one by a major third. Let`s see an example in D minor. The chords are: Dm, Bbm, F#m, Dm. The semitone movements are repeated 3 times, to get back to Dm, because 3×4 =