Means for using visual representation are essential to pattern analysis. Astronomy and mathematics are intertwined through observation and calculation, whether it is via the phases of the moon and periodicity, or constellations and myths. But above all, cave paintings (for a book reference see Ruspoli re Lascaux France) show the way humans interact with nature by composing images.

Five thumbnail images follow and link to some full-size images or other files. Other pointers either display text related to the visual information or tables of pointers leading to related images.



Beach House
twelve-sided solid

inscribed circles

Images are at the heart of some current technological tools. Presentations are made lively via visual material. Charts, graphs, tables, outlines, maps, color, animation, and visualization materials enrich talks/reports.

The web has changed interactions around the globe ... and the resources we share. Computers make the spinning world easy to show, and an image of the whole earth visible (courtesy of Tom Van Sant). Imaging and communication technology let us see how the earth looks from space satellites. Internet exchange of information enables posting a newspaper photograph so it is available for future use. See, e.g., Clifford Ross item below.

Weather Satellite View
potted plant
China 1998
new high-detail camera
© Clifford Ross 2004 All rights reserved;
NY Times 12/9/04 Ross Information
The scientific value of images appears in newspapers, as in the pairing of images by The New York Times May 9, 2006:

In images published
by Science
(from the Earth Sciences
and Image Analysis
Laboratory of NASA)
"An image of Titan,
a moon of Saturn,
top, shows lines of
dunes like those in the
Namib Desert in Africa"
NY Times, 5/9/06
View image pair

Numbers have long fascinated people. One starting as a word in a poem led to an image. Charles Demuth's painting The Figure 5 in Gold completed in 1928, was inspired by his friend's poem The Great Figure. He included the word "Bill" at the top left of the painting, to include the poem's author in the new image. William Carlos Williams poem begins:

Among the rain
and lights
I saw the figure 5
in gold
on a red
fire truck

A game played worldwide,
especially in Africa,
follows (below left).

Links below
are for games, puzzles,
and connections to fractions.

Twelve/Five View
Numbers Text


Running Shoe
Beach House^
^greater detail
Half Dome
La Plata
Street Lamp
Hancock Park
Wawona Hotel*
*greater detail
Vin~a Fruit
Rock Garden
+greater detail

5/14/06 Version
©2006 Allen Klinger