Xah Math Blog Archive 2013-09 to 2013-09

laplace transform formula

Abuse of Math Notation

homeomorphism, and homotopy for 1/z

“homeomorphism” (aka “topological isomorphism”, “bicontinuous function”) is a continuous function between topological spaces that has a continuous inverse function.


In topology, two continuous functions from one topological space to another are called homotopic if one can be “continuously deformed” into the other, such a deformation being called a homotopy between the two functions.


is there a homotopy that maps identity in the complex plane to 1/conjugate[z]? or sin[z]?

Complex Inversion

i think there is. It's obvious, that if the 2 spaces are topologically equivalent, there always is, the question is to find the homotopy. In my case, just use the idea of Geometric Inversion. Let p be the point in domain and p' in range, then just smoothly swap them by gradually narrowing their distance.

Twin Prime Conjecture Breakthru: Yitang Zhang

grid inversion3

The Geometric Significance of Complex Conjugate (updated)

The Significance of Complex Numbers: Frobenius Theorem

the Nature of Associative Property of Algebra


Understanding Complex Numbers

polynomial roots crops

The Beauty of Roots

the meaning of the word variety is varied. There's variety show, then there's algebraic variety. The variegation and etymology is fantastic, not to mention manifold.

show your calculator to Euler and Gauss. Best Scientific Calculators


Maze and Math in Video Games (old essay. Added YouTube videos)

The TeX Pestilence (Why TeX/LaTeX Sucks) (updated)

one of my hero. Willard Van Orman Quine (1908 to 2000). A logical positivists, a logician.

math formula MathJax

9 Tools to Display Math on Web (updated)

Incredible Mathematician John Baez

one of the most fruitful thing g+ has ever done for me since its beginning is discovery of John Baez.

He's a mathematician, and also a well-known writer (even before blog days) He writes a lot, but even when writing research level math, he made it easy for undergrad to understand. And, takes the time to write the interesting aspect, and answer and discuss with your comments/questions. (thus, comments on his post/blog are often very high quality as well) I see that he also sometimes write non-math related things, that touches on history, art, linguistics, all in a very appetizing way with quality/rare photos (and yet not the trite, mundane, beaten-horse types you find daily from social networks). Incredible!

you can read his bio on wikipedia and also follow links to his blogs. John Baez

i'm learning lots stuff from John C B. Lots thoughts hard to summarize nicely.

For one thing, related to SEO, is that it solidifies the idea that in order to get more readers, one should really focus on readers — so-called “engagement”. For example, say, instead of writing 4 posts per day, write just 1 and put the time of the 3 into that 1, to include quality image/illustration, answer questions, iron-out hand-waving. In other worlds, this is really the road for professional blogger. (you might not want to have lots readers, or shudder from the idea of wanting to be “popular”. But if you write publicly, more readers is positive in psychological and practical and philosophical ways. “Readership” defines “authorship”.)

JCB is also pulling me back into math. Such a black hole of pure beauty. The depth of which tantamount the very question of existence and universe.

JCB also sets a good example of doing good in a solid way. (as opposed to the countless shallow and crowd-pleasing blogs, exemplified by the marketing droids of Google of recent years (For example, Google Science, Google Doodle, Google pro-lgbt, …), and countless fanatical “left-leaning liberal” American slackavitists daily pushing their selfish-opinions in the name of greater good.)

Math Formula For Beauty

logic and linguistics. The Logical Levels of Interpretation

karcher je st
Karcher JE Saddle Tower

Dead Reckoning in a Non-Orientable 3D Space

Geometric Dissection, Mechanical Iris, Expandable Table Furniture 📺 (updated)

GeoGebra No Longer FSF Free Software

GeoGebra was open source (GPL) for about 10 years (up to version 4.0), but since version 4.2, now only for non-commercial use. This is bate and switch, but the problem is really open source. When it gets big, it needs funding, but nobody wants to pay.

Here's quote from Wikipedia GeoGebra on its licensing:

Most parts of the GeoGebra program are licensed under GPL, making them free software. However some parts, including the Windows and Mac installers, have a license which forbids commercial use and are therefore not free software.[9][10][11] In practice, this means that non-commercial use by teachers and students is always free of charge, while commercial users may need to pay license fees. For details see the GeoGebra license description.[9]

Since July 2010 the Debian GNU/Linux distribution offers a free version of GeoGebra 4.0 in which all un-free parts of the program were removed or replaced by free software. This version may be used for commercial purposes without paying licensing fees. However, starting with version 4.2 since December 2012, the license is changed to be more restrictive[11] so that GeoGebra cannot be included in Debian GNU/Linux any longer. On the other hand, the software can still be downloaded from its official download page free of charge for many platforms (including Debian as well).

GeoGebra is a Java Applet. But since Apple Apple killed Flash in 2010, as well as not including Java, Java applet is pretty much dead (it doesn't run on any Apple iOS nor Google Android phone/tablet).

GeoGebra just came up with a tablet version from a KickStarter project that got funding of $12k from 310 backers. 〔http://www.kickstarter.com/projects/geogebra/geogebra-for-the-ipad/posts/488589 〕.

60 Plane Curves GeoGebra Files

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