# Rectangle Method for approximating an integral has been rediscovered!

1. Jul 13, 2012

"Rectangle Method" for approximating an integral has been rediscovered!

http://care.diabetesjournals.org/content/17/2/152.abstract

Is this some kind of joke? Has anyone else seen this article before?

This is what I felt like after reading it:

2. Jul 13, 2012

### Dickfore

Re: "Rectangle Method" for approximating an integral has been rediscovered!

She called it after herself. That's modest enough.

3. Jul 13, 2012

### Dickfore

Re: "Rectangle Method" for approximating an integral has been rediscovered!

I found this:

Mary M Tai's Response (it's a PDF)

EDIT:
It's pretty popular on the Internet:
Reinventing the wheel

Last edited: Jul 13, 2012
4. Jul 13, 2012

### Curious3141

Re: "Rectangle Method" for approximating an integral has been rediscovered!

OK, I'm going to publish another paper employing Simpson's Rule (but not call it that), prove it's better or faster-converging than her approximation, and name it after myself.

Seriously, this is embarrassing. Well, she and the referees of the journal should be embarrassed.

5. Jul 14, 2012

### Jimmy Snyder

Re: "Rectangle Method" for approximating an integral has been rediscovered!

This reminds me of a story I once heard of an article on economics that was published in some journal. A mathematician wrote in to point out a simple typo in one of the equations. I don't remember the name of the mathematician, but say it was Smith. The corrected equation then came to be known as Smith's law.

6. Jul 14, 2012

### Drakkith

Staff Emeritus
Re: "Rectangle Method" for approximating an integral has been rediscovered!

I'm not sure I get it. Doesn't calculus do this already? (My knowledge of calculus comes from reading part of a Calculus for Dummies book)

7. Jul 14, 2012

### AlephZero

Re: "Rectangle Method" for approximating an integral has been rediscovered!

Why should it be surprising that nutritionists don't know calculus? Hey, you can even study physics without calculus these days, except it's more politically correct to call it "algebra-based physics" not "calculus-free physics".

At least what she did was right. I've seen much worse nonsense perpetrated by people who shouldn't have been allowed anywhere near inventing numerical methods.

8. Jul 14, 2012

### Astronuc

Staff Emeritus
Re: "Rectangle Method" for approximating an integral has been rediscovered!

Hmmm - I remember using the technique in 1974-1975 - during a calculus class in high school. We also studied the trapezoidal and Simpson's rules - and the Riemann sum. Later at university (70s and 80s), we delved more into the theory behind quadrature as part of a course on numerical methods which included various quadrature, or numerical integration, techniques.

9. Jul 14, 2012

### BobG

Re: "Rectangle Method" for approximating an integral has been rediscovered!

I would have been more impressed if she had reinvented this method:

http://www.ehow.com/how_6209482_calculate-acreage-map.html [Broken]

She could have determined the area of the entire graph and weighed it.

Then she could have cut out the area under the curve and weighed that.

Simply brilliant!

Last edited by a moderator: May 6, 2017
10. Jul 14, 2012

### Dickfore

Re: "Rectangle Method" for approximating an integral has been rediscovered!

Question: How does one plot the curve exactly according to its functional form?

Last edited by a moderator: May 6, 2017
11. Jul 14, 2012

### BobG

Re: "Rectangle Method" for approximating an integral has been rediscovered!

So that a computer can search through its database to find similar shapes?

That's a pretty tough task (and one I've never done myself, even though I've used the results of that type of analysis). Review of shape representation and description techniques

It's a lot tougher than just comparing the areas unders the curves.

But analyzing the shape itself can be pretty important for a lot of tasks, such as determining orbital perturbations on satellites due to oblateness of the Earth, "bulges" around the equator, etc. with Legendre polynomials being most common method for geodysey (Earth geoid)

12. Jul 14, 2012

### Reptillian

Re: "Rectangle Method" for approximating an integral has been rediscovered!

Somebody needs to teach this woman about Runge-Kutta.

13. Jul 14, 2012

### 256bits

Re: "Rectangle Method" for approximating an integral has been rediscovered!

Is there a limit to the maximum number of times New York can be repeated in the address?

14. Jul 14, 2012

### Q_Goest

Re: "Rectangle Method" for approximating an integral has been rediscovered!

It's worse than you think! (Read the paper)

Apparently, Mary Tai doesn't know how to calculate the area of a trapezoid (and thus employ the trapezoidal rule). Instead, Mary calculates the area of a rectangle (Simpson's rule) and then modifies it by ADDING the area of the remaining triangle.

So yea, this is an original work. I can't remember calculus courses teaching this particular method!

15. Jul 14, 2012

### Dickfore

Re: "Rectangle Method" for approximating an integral has been rediscovered!

16. Jul 14, 2012

### Dickfore

Re: "Rectangle Method" for approximating an integral has been rediscovered!

So, in conclusion, your method fails.

17. Jul 14, 2012

### AlephZero

Re: "Rectangle Method" for approximating an integral has been rediscovered!

Solving a differential equation (with automatic error estimation and step size control) can be an excellent way to do numerical quadrature.

Last edited by a moderator: Jul 14, 2012
18. Jul 16, 2012

### someGorilla

Re: "Rectangle Method" for approximating an integral has been rediscovered!

I guess that paper has been referenced already a lot of times. Nice way to increase your number of citations! While giving people a good laugh, what more do you want?
And who knows, she might patent the method. It's not new? Of course it's new, this is specifically for metabolic curves. There's a lot of patents like that, like the sled for carcasses.