This mini-web site is devoted to the geometry problems created by my friend Hirotaka Ebisui, a Japanese mathematician who turned elementary geometry into the most exciting adventure in life of many peoples. I will enclose here interactive version of a few of his problems, short information about Hirotaka Ebisui, as well as some background information.

All, presented here, interactive problems were created using Geometer's Sketchpad. While loading first of them for the first time it takes a few seconds to download in the background the GSP Java file. Then each new file will be displayed without any major delay. Readers do not need to have Geometer's Sketchpad on their computers. Properly working Java is the key to get all necessary interactivity.

I guess, some users may want to create their own versions of Hirotaka problems. In such case I suggest to download Geometer's Sketchpad from http://www.keypress.com The evaluation version will give you a pleasure of opening each of enclosed here GSP files and see how they were created, expand them or add your own problems.

Convention

While developing interactive examples I used the following convention.

• Medium thick lines, green, are the starting point of the construction.
• Thin lines, usually blue, sometimes dashed, are the construction lines. In many cases, if these lines are not needed any more, we hide them. However, sometimes I leave them in order to show better how the construction was done.
• Thick, red lines, are the final ones that usually carry some property to be proved or are part of the final object, e.g. a triangle, rectangle, etc., with specific properties to be proved.
• Small, blue points: Usually I hide all points that do not matter for the whole construction. I leave only selected points to emphasize some important features, e.g. point on a segment, on a circle, etc. These points are usually small with light blue filling.
• Medium size points with yellow filling are those construction points that in GSP file, or in GSP online applet, can be moved in order to check what will happen with the property to be proved.
• Fills do not follow the above convention. I added them in order to make these constructions similar to the Edo period sangaku pictures.
• The numbers for each problem are the original numbers used by Hirotaka Ebisui. In order to avoid some confusion there is one thing that we should mention here. It may happen that a few of his constructions may carry the same number, or the same construction may occur in two or more places in his notes each time with different number.