Engineering image systems is moving from display, what was once called computer graphics, and enhancement - computer image processing to get detailed or panoramic information, to day-to-day usage. Terms like the world-wide-web, havegeneral-audience implications, appear in daily newspapers and weekly newsmagazines (and not just in science articles but in many advertisements),even though the technology didn't exist a few years ago. That makes our entire

society interested in why it takes so long to transfer an image from a remote computer where it exists as a data file to the personal computer where it is displayed by an internet browser program. In short, there has to be a new focus to technical work, and it must serve the users who interact with image data on computers, people, some of whom may be schoolchildren, who are

connected by existing systems to digital archives containing visual, auditory, and textual information.

Interactivity means many things for computing. First it changes the technical focus from the processing side to the user's needs. This article presents a series of issues associated with enabling users to to rapidly understand the essence of a visual image. That focus on computer systems to transmit visual data creates technical design needs. However the needs involve new directions in the associated fields, and it will be necessary to redesign engineering education to prepare for the work that must be done.

Traditionally engineering uses many kinds of image models: line-drawings, sketches, and diagrams are used heavily in the traditional curriculum. Many technical achievements - *e.g*., image data from space probes and satellites, computed medical images from x-ray, nuclear-magnetic-resonance, positron-emission, ultrasound sensing - involve creating photographic

representation. Likewise, through high-speed computers and high-resolution displays, the field of simulation - computer-generated data models - has taken on new power. For example, fluid flow and other dynamic data fields can be shown on computer monitors. That kind of activity is called visualization, the graphic modelling of numerical information as an animated time-evolving set of pictures. One type of extension of education through computer-networks is creating geographically-diverse databases of such pictures that are accessible from any place having world-wide-web access. Another, is the identification of key issues in education that can best be explained by imagery, and creation of meaningful sets of pictures keyed to school topics in Mathematics and other domains.

1. Showing.

a. Images are central to design.

b. Pictures, graphs, diagrams are fundamental tools for furthering

group projects.

c. Images as communication tools.

**2. Understanding.**

a. Visual puzzles demonstrate fundamental knowledge.

b. Words, signs and symbols as shorthand.

c. Education as "learning the shorthand and lacking the knowledge."

**3. Potential.**

a. Computing as an activity of possibility.

b. Gates that are doorways, symbols that are moats.

c. Involvement and exploration.

4. Experimentation.

a. Using the world-wide-web as an educational resource.

b. Requiring visual presentations.

c. Challenge by demonstration that firmly-held beliefs are overly-restrictive.

**5. Creativity.**

a. Stimulating computer use.

b. Using writing tools.

c. Requiring cooperative class activities.

1. Calculating a slowly-converging infinite product to greatest possible exactness. See URL {1}.

2. Odd/even via cube as a sum of consecutive odd numbers.

8 = 3 +5; 27 = 7 + 9 + 11; use images of 8 cubes, 27 cubes (available)

3. Exponential power via wrapping friction example. New digitized photo of paper clip example: balances a large weight if nylon cord is wrapped around a finger.

4. Data structures via matrices and tetradecahedron display. Images - see URLs {2, 3}. Use Mathematica representation and new displays showing analytic geometry points in 3-space that are vertices of the solid.

5. Baseball arithmetic. See book reference [1] and the real case where (1/2) + (1/3) does = 2/5, namely batting averages.

6. Calculating pi - Newton's first giant achievement. See book reference [2].

7. Cathedral of Gaudi, hyperbolic cosine, inverted catenary. Mathematics as a central element of design from the Hagia Sophia in Istanbul with parabolic vaults, to the in-construction in Barcelona lighter towers based on these exponential curves.

8. Binary representation. Nine apples to be distributed to four baskets, an odd number to each.

9. Holding alternate viewpoints: half of eleven is six, nine dots four lines. See book reference [3]. Tie this to 8. Since binary eleven is 1000 + 11 , namely 1011, so half is 10 ( = 2) or 11 ( = 3).

10. Arithmetic combination examples. *Dates: *Things like: 1 17 97: -1 + 17 = 9 + 7 *Digits*:

Combining every one of the digits from 1-9 so that they equal 100: The digits, 1-9, must be arranged in order, and individual digits may be used together to form a number. If that (digit-adjacency) is not done,parentheses, plus, minus, divides, and times symbols may be inserted. Two examples are:

1 + (2*3) + 4 + 5 + (67) + 8 + 9 = 100; 123 + 4 - 5 + 67 - 89 = 100; while R. Gurfield found:

(1 - 2 + 3) * ( - 4 - 5 - 6 + 7 * 8 + 9) = 100; (1 - 2 + 3) * (4 * 5 - 6 * 7 + 8 * 9) = 100

11. Relations to computer readiness. People who have no idea about things like playing card probabilities, behavior of dice, relative sizes of or differences between a billion and a million, baseball/football/basketball statistics, and other such things are ill-prepared to work with pointers, hierarchy, cut and paste and other basic computer concepts.

{1} http://www.cs.ucla.edu/csd-lanai/fweb/cs190/nsf_ehr_pro_latest.html

{2} http://www.cs.ucla.edu/csd-lanai/fweb/cs190/tet1.TIF

{3} http://www.cs.ucla.edu/csd-lanai/fweb/cs190/tet2.TIF

[1] Kline, Morris, *Mathematics for the Nonmathematician*, New York: Dover, 1967.

[2] Dunham, William, *Journey Through Genius: The Great Theorems of Mathematics, *New York: John Wiley & Sons, Inc., 1990.

[3] Adams, James, *Conceptual Blockbusting*