The kernel of the dabanese syntax uses just four notions: dabagram (dabanese ideogram), unordered phrase, ordered phrase, accent (subject). The language is governed by very simple syntax rules.

# Dabanese — a general introduction

an international language for written communication

Other dabanese knols are listed here: Dabanese–index. Dabanese is an international language for written communication, which I have been developing (not intensively) since the spring of 1985. Dabanese has a lot in common with the written Chinese language. In particular, dabanese like Chinese uses ideograms. The dabanese ideograms are called dabagrams. At this time (october […]

Dabagram entries which possibly are not yet in their final form.

The original goal of the theory of diophantine approximations is to study how well different real numbers can be approximated by rational numbers in terms of a relation between the precision of the approximation and the size of the denominator of the approximating fraction. The most difficult real numbers x to approximate by rational numbers different from x are rational numbers x. Then the worse x is the so-called golden ratio Φ and irrational numbers related to Φ in a certain way. Almost as bad as Φ are the so-called quadratic irrationalities like √2.

This knol introduces two of the basic notions of the theory of diophantine approximations: 1. pairs of fractions which are neighbors, and 2. the LU encoding of the non-negative real numbers. Only their very first properties are provided in this knol. More advanced properties will be presented in the next knols.

An index of my knols related to mathematics (it starts with “General”, and then the main topics are listed in the alphabetical order); see the details and click on the links just below, in the “Contents”, or on more detailed links in the main body of this knol, below “contents”.

There will be more to come, I hope. Also, an extensive (but not complete) list of outstanding mathematicians (and other scientists, artists, etc.) is included in my knol “WhoWheWha”, which tells you: who? when? what?

# Reflections on mathematics (migma)

My view and sayings about mathematics (migma)

I have posted my first migma in 1994 (years after I made it up), on sci.math, when there was a discussion “*** Definition of Mathematics ***” ;. and my second migma on pl.hum.poezja, in 2001. The remaining ones (and the first two too) I posted on my page:

http://www.alanisko.com/wlod/mthFrames.html

in 2004, and some of them, in Polish, on pl.hum.poezja, where these migma started a discussion about the material (physical) nature of mathematics, etc., during the week++ from 2004-Oct-23 to Oct-31, with Polish poet Przemysław Łośko being especially involved, and presenting his deep, independent views, which had quite a bit, even a lot in common with my own.

Migma is both singular and plural.

# Special characters & HTML strings

Greek, Polish and Mathematical letters, Russian keyboard, and symbols + html strings

Greek letters, mathematical symbols, and other, are listed here, so that one can relatively easily copy them and paste into their knols or other files (let me know if you want me to add some more, I might).

Several proofs of the infinitude of the set of all primes, starting with the original proof by Euclid.

# Reference

wh reference knols

# Geometric progression

Geometric progression, and Number Theory too.

The geometric progression (g.p.) has the distinction (or stigma?) of belonging to the elementary and high school curriculum. The infinite g. p. plays its role also in Mathematical Analysis and especially in the theory of analytic functions. It is less commonly noted that geometric progressions appear in Number Theory, starting with the Mersenne numbers 2^n – 1 = 1 + 2 + … + 2^(n-1). Mersenne numbers occur in the Euclid-Euler characterization of even perfect numbers, as the sums of divisors of powers 2^(p-1). In general, the sum of divisors σ(p^n), when p is a prime, is the sum of a geometric progression 1 + p + … + p^n, hence the connection between g.p. and the number theory, which motivates a close look at the algebraic properties of a g.p. The standard geometric progressions generalize the Mersenne numbers (here “standard” means that the initial term is 1).