A New Look At Geometry

What Hacker News says

1. a_pApr 2013
   Perhaps you haven't heard about the doctor who rediscovered the trapezoid rule and had his article published in a respected, peer reviewed biology journal in 1994.[1] The paper is called "A mathematical model for the determination of total area under glucose tolerance and other metabolic curves" — and it got 75 citations (as of 2007). EDIT: Google Scholar lists 178 citations now [‽]. The 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."

   More information about it is available here. [2]

   EDIT: I just looked at the full article and it is more bizarre than I had anticipated. For one, it says that "three formulas have been developed to calculate the total area under a curve", and then lists the works in which the formulas are given. One of the works listed is Irving Adler's A New Look at Geometry, which is a math book accessible to readers with a high school education (it's good book by the way — the MAA has given it a rating of BLL [3]). But Adler's name is misspelled "Alder" in the article and in the citation. The author also gives credit to a doctor at Yale for "his expert review". How embarrassing.

   [1] http://care.diabetesjournals.org/content/17/2/152.full.pdf+h...

   [2] https://fliptomato.wordpress.com/2007/03/19/medical-research...

   [3] http://mathdl.maa.org/mathDL/19/?pa=reviews&sa=viewBook&...

   [‽]http://scholar.google.com/scholar?q=A+Mathematical+Model+for...

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2. dpqMar 2021
   The paper in question can be found with Sci-Hub. Amusingly enough, it contains the following:

   > Three formulas have been developed by Alder (3), Vecchio et al. (4), and Wolever et al. (5) to calculate the total area under a curve

   [3] Alder I: A New Look at Geometry. New York, The John Day Company, 1966.

   This book is in turn available in archive.org:

   https://archive.org/details/B-001-001-934/page/n269/mode/2up

   So basically the author in question didn't even bother to read the relevant part of the book she referenced, and also misunderstood the explanation of the Area and Integral chapter as something that Irving Alder developed.

   I didn't bother looking up the other two references to help preserve my sanity.

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