Tai's model

An animation showing how the trapezoidal rule approximation improves with more divisions.

In 1994, nutrition scholar Mary M. Tai published a paper in the journal Diabetes Care entitled "A Mathematical Model for the Determination of Total Area Under Glucose Tolerance and Other Metabolic Curves". In the paper, Tai puts forth her discovery of "Tai's model", a method of estimating the area under a curve by dividing the area into simple polygons and summing their totals. Apparently unbeknownst to Tai (or her peer reviewers and publisher), her "discovery" was in fact the trapezoidal rule, a basic method of calculus that has been used as far back as before 50 BCE by Babylonian astronomers.

Several mathematicians replied to the paper in letters to the journal, objecting to the naming of "Tai's model" and the treatment of a method "used in undergraduate calculus courses" as a novel discovery in the field of diabetes care. A letter entitled "Tai's Formula is the Trapezoidal Rule" also pointed out errors in Tai's representation of the underlying mathematics (such as referring to a count of square units below the curve as the "true value" of the area) and problems with the method's applicability to glucose tolerance curves, which are already approximations.

Tai responded to the letters, saying that she'd derived the method independently during a session with her statistical advisor in 1981—noting that she had a witness to the model's originality. "The concept behind [Tai's model] is obviously common sense," wrote Tai, "and one does not have to consult the trapezoid rule to figure it out." She explained that her decision to publish her derivation was at the request of her colleagues at the Obesity Research Center, who'd begun using her model and called it "Tai's formula". Tai's colleagues wished to cite the formula, she explained, but could not do so as long as it remained unpublished, and thus she submitted it for publication. Tai attempts to distinguish her model from the trapezoidal rule on the basis that Tai's model is based on the summed areas of rectangles and triangles rather than trapezoids. A follow-up letter by the authors of "Tai's Formula is the Trapezoidal Rule" points out that each contiguous rectangle–triangle pair in Tai’s construction actually forms a single trapezoid.

"A Mathematical Model for the Determination of Total Area Under Glucose Tolerance and Other Metabolic Curves" has been cited over 500 times as of March 2025, "likely in jest by further researchers who needed to use the trapezoidal rule" according to science writer James Felton.

The episode has been cited as an illustration of the half-life of facts.