September 10, 2002

NOTE TO JOURNALISTS: Inquiries on obtaining review copies of the book should
be directed to Cathy Siddiqi, Cambridge University Press, 40 West 20th St.,
New York, NY 10011; (212) 924-3900, ext. 323.


WEST LAFAYETTE, Ind.  It's not a nostalgic return to the '50s and '60s, but
a Purdue University professor's new book still may have readers doing the

Greg Frederickson's book, "Hinged Dissections: Swinging and Twisting,"
delves into a world in which triangles can be transformed into squares,
crosses into hexagons, and back again  all with the grace of dancers
swinging around a ballroom floor.

True to its subtitle, Frederickson's book illustrates how geometric figures
can be cut into pieces, which are then attached to one another by hinges
that allow the pieces to swing into new positions and form a different
figure. Mathematical puzzles like these were popular in newspapers around
the turn of the 20th century. Although a few of these dissections were known
to work with hinges that have a swinging motion, Frederickson discovered
enough new hinged dissections to fill a whole book.

Yet this professor of computer sciences (and, incidentally, a child of the
60s) added a new dimension by including the idea of "twisting."

"Instead of simply swinging pieces on a flat surface, I discovered a new
kind of transformation that relies on twisting around the pieces in three
dimensions," Frederickson said. "It boggled my mind when I realized that I
could twist around a set of pieces to form, for instance, either a square or
an equilateral triangle."

"Hinged Dissections: Swinging and Twisting" will be published by Cambridge
University Press this month at a price of $45. "Dissections: Plane and
Fancy," Frederickson's earlier book on unhinged dissections, appeared in

With more than 500 illustrations and whimsical prose suggesting a vivid oral
presentation, Frederickson takes the reader on a remarkable journey from the
simplest of geometric puzzles to complex transformations involving solid
objects. Along the way, the author highlights the colorful history of the
field and explains the methods with which he has created hinged dissections.
One method uses tessellations, which are repeating patterns formed from
identical tiles.

"Readers may be familiar with tessellations from some of the lovely work of
the artist M.C. Escher," Frederickson said. "My book takes off in a
different but equally fascinating direction of using the symmetry of the
tessellations to create hinged dissections."

Frederickson, whose specialty is designing computer algorithms that use a
minimum of time and memory, found that the emphasis on efficiency in his
research spilled over into his passion as he tried to minimize the number of
pieces in his transformed shapes. He is equally motivated by a fundamental
curiosity about how geometry and motion interact.

"These issues are also addressed by researchers who think about packing
objects compactly into space launch vehicles," he said. "Once the object has
been transported up into space and is ready to be deployed, it may need to
be unfurled or otherwise transformed into a desired configuration, using
hinged motion."

Aside from the possible applications, however, Frederickson swings figures 
and writes books about this unusual activity  for a much simpler reason.

"It's great fun," he said. "Try it, and you'll find yourself swinging, too."

Writer: Chad Boutin, (765) 494-2081, [EMAIL PROTECTED]

Source: Greg N. Frederickson, (765) 494-6016, [EMAIL PROTECTED]

Related Web sites:

Book Web site:

Movies of swinging pieces:

Photos of a square/triangular table made from swinging pieces:

Jeanne Norberg, director
Purdue University News Service
1132 Engineering Admin. Bldg.
West Lafayette, IN 47907-1132
Office: (765) 494-2096;      Fax:  (765) 494-0401
Pager:  (765) 423-8662;      Cell: (765) 491-1460
Home:   (765) 449-4986

Reply via email to