# Scooped … by Newton and Leibniz

A Mathematical Model for the Determination of Total Area Under Glucose Tolerance and Other Metabolic Curves

Abstract

OBJECTIVE To develop a mathematical model for the determination of total areas under curves from various metabolic studies.

RESEARCH DESIGN AND METHODS In Tai’s Model, the total area under a curve is computed by dividing the area under the curve between two designated values on the X-axis (abscissas) into small segments (rectangles and triangles) whose areas can be accurately calculated from their respective geometrical formulas. The total sum of these individual areas thus represents the total area under the curve. Validity of the model is established by comparing total areas obtained from this model to these same areas obtained from graphic method Gess than ±0.4%). Other formulas widely applied by researchers under- or overestimated total area under a metabolic curve by a great margin.

RESULTS Tai’s model proves to be able to 1) determine total area under a curve with precision; 2) calculate area with varied shapes that may or may not intercept on one or both X/Y axes; 3) estimate total area under a curve plotted against varied time intervals (abscissas), whereas other formulas only allow the same time interval; and 4) compare total areas of metabolic curves produced by different studies.

CONCLUSIONS The Tai model allows flexibility in experimental conditions, which means, in the case of the glucose-response curve, samples can be taken with differing time intervals and total area under the curve can still be determined with precision.

That’s right — the author discovered the trapezoidal rule from integral calculus and named it after herself. A subsequent issue of the journal contained several letters pointing this out. (Both links may be paywalled for all I know.)

It’s pretty embarrassing that such a paper (a) got written in the first place and (b) passed peer review, but  the really shocking part is that the paper has garnered 161 citations. ### Ted Bunn

I am chair of the physics department at the University of Richmond. In addition to teaching a variety of undergraduate physics courses, I work on a variety of research projects in cosmology, the study of the origin, structure, and evolution of the Universe. University of Richmond undergraduates are involved in all aspects of this research. If you want to know more about my research, ask me!

## 2 thoughts on “Scooped … by Newton and Leibniz”

1. Bre says:

That’s not even calculus. The trapezoidal rule dates to antiquity.

2. Ted Bunn says:

You’re quite right. I should have said “scooped by Archimedes,” probably.