Blog on The Wonderful World of Organic Geometry

Testing Ganja code

Tue, 11 Mar 2025 00:00:00 +0000

Testing ganja code in html #

On this page I want to test including ganja code directly in the post. This will allow me then to convert the ganja notebooks that I have created into Hugo pages.

You can drag the center of the animated circle.

Sample page

Fri, 17 Jan 2025 14:05:11 +0100

A sample page #

In this post I am checking out the capabilities that are needed for visualizing mathematics.

For example, $\LaTeX$:

\[ \begin{aligned} KL(\hat{y} || y) &= \sum_{c=1}^{M}\hat{y}_c \log{\frac{\hat{y}_c}{y_c}} \\ JS(\hat{y} || y) &= \frac{1}{2}(KL(y||\frac{y+\hat{y}}{2}) + KL(\hat{y}||\frac{y+\hat{y}}{2})) \end{aligned} \]

Interactive GeoGebra demo #

Here is a GeoGebra demo of Pascal’s theorem. You can’t access the main menu but you can use the construction tools. First we show both in a 2-column format. Unfortunately the GeoGebra borders are huge and I don’t know how to omit them.

Organic geometry

Tue, 14 Jan 2025 00:00:00 +0000

The rise of a new geometry #

Girard Desargues (1591-1661), mathematician, architect and engineer, discovered a new and intriguing geometry, which he reported on in the short book “Rough draft of an essay on the results of taking plane sections of a cone” (1639). Introducing new concepts into geometry related to the rise of perspective painting, the book provided startling new proofs of Apollonius’s classical results on conics. Desargues’ work was far ahead of its time, and vanished almost without a trace soon after his death.