28 September 2020

I restart my blog—I would like to disseminate some recent results and ideas. For that I redesigned my webpage using a kind of \(\TeX\)-style.

I expect that the following features are present:

• Easy way to communicate mathematics. For that purpose I will use MathJax.
• Nice look. For that I will use Computer Modern Fonts.
• Embedded GeoGebra applets. In fact I would like to use some extra features from GeoGebra Discovery.

Here is a simple GeoGebra applet:

To try some new features, please follow these steps:

1. Click on the 5. toolset in the Toolbar and select the second tool (Regular Polygon ).
2. Draw a segment in the Graphics area (on the right) by clicking twice.
3. GeoGebra will ask the number of vertices of the regular polygon to draw. Enter 4.
4. Click on the 8. toolset in the Toolbar and select the last tool (Discover ).
5. Click on point \(A\).
6. After a few seconds you should see a report on Discovered theorems on point \(A\). You can safely close the popup window by clicking OK.
7. Click again on the 8. toolset in the Toolbar and select the last but one tool (Relation ).
8. Click on \(AB\) and \(AC\), and then click More.... Now you are reported that it is generally true that the ratio between them is something like \(|AB|=\frac{\sqrt2}{2}\cdot|AC|\).

You can find some further information on this topic in the arXiv paper Towards Automated Discovery of Geometrical Theorems in GeoGebra (co-authored with Jonathan H. Yu).