Arthur Lemlich The Roosevelt Hospital Hans H. Zinsser
Columbia University New York, New York
A Method of Visual Representation
of Three-dimensional Functions
The current advances in chemical and chemical engineering theories require the use of increasingly more complex mathematical formulations. Visual representations are very useful in presenting these mathematical concepts to the student.'
Figure 1.
Legointerlocking
co-exist with pregnancy, enlarged prostate, and anatomical abnormalities of genito-urinary tract was investigated with the aide of computer-assisted statistical techniques. Four hundred cases of this disease were reviewed for approximately 400 factors each, and an IBM 7090 high meed c o m ~ u t e rwas used to execute p~rtinentstnti~ticalyrognms. The outpiit of these prngranis consisted of :mays of numhrrs, or nutrirrs, rqiwv!nting the vomplcx ilitrrrelationsliil,.i of the fnctors studied. A useful presentation of this complex data was accomplished by the use of described system (Fig. 2).
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blockr.
Two-dimensional, as well as certain simple threedimensional phenomena, can be represented effectively with graphs. However, complex three-dimensional systems are best rendered by three-dimensional scaled models. Several methods for construction of such models were investigated. Accuracy of representation, rapidity of assembly, and flexibility of each system were considered. Lego2 system of interlocking blocks (Fig. 1) was found to be quite satisfactory. This system consists of scaled precision cast plastic blocks available in many shapes and colors. This system was used to represent visually a series of complex statistical relationships derived from a large scale computer-supported study described below.8 Infection of the kidney, or pyelonephritis, a complex end multifaceted disease, occurring in both males and lemales in all age groups, and particularly prone to 'ZINSSER, HANSH., THIS JOURNAL, 31,662 (1954). "Lego System" of interlocking blocks made b?r Shwa~er Bros., Inc., Denver, Colorado. R., LEMLICH, A., AND ROOT,L., 'ZINSSER,H. H., BONNER, 'Pvelonephritis: A study of Disease in Depth," Proc. 4th IBM ~ e d i e a ~l ~ m ~ o s i u~ndicott, m, Kew York, fiavember, 1962.
Volume 41, Number 3, Morch 1964
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American Medical ~ s o c i o t ' & n~ o n v m t i o nhtlantic , c i t y . June,
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Figure 3. Left: Model o f a normal density function of one variable Right: Model d a bivoriote normal density function.
The visual representation of energy surfaces, kinetic models, statistical distributions (Fig. 3) and other mathematical and physical concepts used in chemistry and chemical engineering may he accomplished by this method.
