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    1. #1
      Rational Spiritualist DrunkenArse's Avatar
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      Theoretical Diabetes Researcher Makes Groundbreaking Mathematical Discovery.

      This come up on another forum that I read and I thought that some people here would like it. It doesn't quite compare with some of the work that one of our very own members has done but it's impressive none the less.

      A mathematical model for the determination of total area under glucose tolerance and other metabolic curves.

      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 (less 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.

    2. #2
      Xei
      UnitedKingdom Xei is offline
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      Hahahaha... wow.

      I love how the entire theory apparently only applies specifically to graphs of metabolism.

      But you're right, this cannot compare to the magnificent feat of squaring the circle.

    3. #3
      Rational Spiritualist DrunkenArse's Avatar
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      Apparently some readers wrote in and a few months later, the journal ran one of them titled "Tai's Model is the Trapezoidal Rule." All the same, if there are seriously medical researchers out there that don't know how to find the area under a curve than part of me can't help but wonder if that is, in at least some small part, responsible for this whole "disease" thing still being around. Quite a few papers referenced this one. In the sciences, that means something. I'm told that it doesn't mean as much in other fields but all the same, enough people found it useful so that there was apparently a gap of some sorts for it to fill. We might be a few years closer to a cure if only they had the tools to properly analyze their data...

    4. #4
      Xei
      UnitedKingdom Xei is offline
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      Wow, I see what you mean.

      That is truly disturbing really... it's also disturbing to think that none of those people realised after two seconds thought that you can find the area under a curve to arbitrary precision with a Riemann sum.

      Also, when he says he checked his answer by comparing to 'graphical methods'... what on Earth does that mean? Did he count the squares or something? Or did he plot the data on a computer and use an area function, which was likely based on the trapezium rule in the first place? The whole thing is so stupid it's funny, but also kind of concerning that people would cite it.

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