[Version in Spanish] [Version in Portuguese] [Version in French]
 Changing the position of the solid below gives different views of its shape. Three of these views generate letters of the alphabet and, with them, it's possible to make a word in english. Rotate the solid (click/touch and drag) and try to find this word! The alphabet below shows the shapes of each letter that can appear in the solid. Be careful: the letters H and I have the same shape. The same occurs with the letters N and Z and with the letters M and W. The letters must be given in the correct order! To input your guess, click/touch on the interrogation marks “?”.
Please wait for the browser to load the page completely. If this has already happened and the applet below has not shown, this means that your browser does not seem to support WebGL or this option is not enabled.

?
?
?

Choose the type of game: Words in English  Words in Spanish  Words in Portuguese  Words in French

 SUPPLEMENTARY NOTES

 BACH, ESCHER E GÖDEL This kind of solid was idealized by Douglas R. Hofstadter to illustrate the cover of his book Gödel, Escher, Bach: An Eternal Golden Braid.

EXPANDING THE IDEA: THE DIGITAL SUNDIAL

Are there objects whose projections include more than 3 letters? The answer is yes! In fact, there is a theorem from the fractal theory that guarantees the following: if you choose a collection of plane pictures (not necessarily letters), there is an object whose projections include the pictures you've specified (except for a set of measure zero).

This theorem is the starting point for the concept of a digital sundial, that is, a clock which displays the time in numbers using only shadows and the light from the sun. Like the conventional sundial, the device contains no moving parts and it does not use electricity. The digits change as the sun moves across the sky.

The idea started in the late 80s (with the mathematician Kenneth Falconer) and, in 1991, it was presented by Ian Stewart in the Scientific American magazine (August edition). A few years later, in 1994, three Germans, Hans Scharstein, Daniel Scharstein and Werner Krotz-Vogel, built the model shown below. The patent may be found here. A portable version of this digital sundial is being commercialized by the company Digital Sundial.

 THE CORK PLUG The object below has three holes in the form of a square, a circle and a triangle. The circle's diameter and the square's side have the same length. The triangle is isosceles and its base and height have lengths equal to the length of the square's side. Is it possible to build a three dimensional solid that can stopper tape these three holes? Click/touch on the image below to see an answer!

 Responsible: Humberto José Bortolossi. Idealization and Programming: Rogério Vaz de Almeida Jr. and Humberto José Bortolossi. Revision: Carlos Eduardo Castaño Ferreira, Igor Bromonschenkel Brandão, Anne Michelle Dysman Gomes, Luis Antonio Brasil Kowada and Tahyz Gomes Pinto. The Trip-Lets VRML files were generated using a program written by Christ van Willigen. Pictures: Wikipedia and Digital Sundial. Spanish version: Fabio Ximeno. French version: Ronald Pierre Alain Pétin and Yves Jean Robert Gounot. Trip-Lets in HTML5 Version 05/03/2017 Updates of this software will be available in the following address: http://www.uff.br/cdme/html5/triplets/triplets-html/triplets-en.html. Alternative address: http://www.cdme.im-uff.mat.br/html5/triplets/triplets-html/triplets-en.html.

 This interactive software was programmed using the JavaScript integrated development environment WebStorm.