Bolyai Memorial in Marosvásárhely

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram CDF Player or other Wolfram Language products.

Requires a Wolfram Notebook System

Edit on desktop, mobile and cloud with any Wolfram Language product.

This Demonstration depicts an open-air sculpture inaugurated on the 200th anniversary of the birth of János Bolyai in Marosvásárhely, Transylvania. It was designed by mathematician Sándor Horváth. The central shape is part of a pseudosphere. Unlike the real sculpture, here you can see the rest of the pseudosphere.

Contributed by: Sándor Kabai and Sándor Horváth (July 2012)
Open content licensed under CC BY-NC-SA



The three parts are the pedestal, a frame made of stainless steel bars, and a bell-shaped plastic piece that is a surface of revolution of a tractrix.

The pedestal suggests the stepped development of the science, and also the six steps symbolize the first six days of the week. The seventh level (the seventh day) is the level of enlightenment, the level of scientific discovery. The tubular structure is a symbol of spacetime: the four triangles stand for four quarter-years (each consisting of three months) and the 12 squares stand for 12 months, (each consisting of four weeks). Also, the skeleton is equivalent to a shape that can be used to fill hyperbolic three-space. The shape was inspired partially by Jeff Weeks's Curved Spaces software.

The piece of a pseudosphere in the middle is the surface that Beltrami discovered was a model of hyperbolic plane geometry.

On an incision in a corner of the pedestal is engraved a quotation from János Bolyai: "From nothing I have created a new, different world”. This quotation is from a letter János Bolyai sent on November 3, 1823 to his father, Farkas Bolyai (also a mathematician), in which the young mathematician announced the discovery of the new geometry. With the help of two hidden mirrors, this inscription is illuminated by the Sun each year on November 3.

The following is written on the monument in Hungarian, Romanian, and English:



[1] Teleki-Bolyai Library. (Jun 27, 2012)

[2] Wikipedia. "János Bolyai." (Jun 27, 2012) C3 % A1nos_Bolyai.

[3] J. Weeks. "Curved Spaces." (Jun 27, 2012)

[4] Wikipedia. "Pseudosphere." (Jun 27, 2012)

[5] Wikipedia. "Pseudosphaera-szobor." (Jun 27, 2012)

Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.