From: richard@fwi.uva.nl (Richard Carels)
Subject: Re: Hoe weten ze dat?
Organization: FWI, University of Amsterdam
Distribution: nlnet
Date: Tue, 8 Sep 1992 08:32:21 GMT

In article <5291@tuegate.tue.nl> johan@blade.stack.urc.tue.nl (Johan Wevers) writes:
> In article <4073@svin09.info.win.tue.nl> paulr@info.win.tue.nl writes:
> 
> >In article <Bu7Fot.KMH@cs.vu.nl>, pakuin@cs.vu.nl (Kuin PA) writes:
> >> Wat ik me afvroeg was is: Hoe weten ze dat de Mont-Blanc 4807 meter hoog is ?
> >> Hoe hebben ze dat ooit opgemeten?
> >
> >Ja, dat gaat als volgt: Meet de lengte van de schaduw van de grote berg (L).
> >Maak een heel klein bergje en meet daar de hoogte (h) en lengte van de
> >schaduw (l) van. Dan is de hoogte van de grote berg gelijk aan h*L/l.
> 
> Dat kan nooit: de hoogte van een berg wordt opgegeven t.o.v. zeeniveau, en
> de voet van de berg is meestal hoger.
> 
> Ik denk dat ze dat via de luchtdruk meten.
> 
Ja, en daar heb je een barometer voor nodig. Hoe dat gaat? Hiervoor moet ik
putten uit mijn rijke verzameling onzin:

There are SEVERAL ways to solve a problem. For example, consider the
following from "The Teaching of Elementary Science and Mathematics" by
Alexander Calandra:

"The process of creativity is a mysterious and interesting one. It is
brilliantly described in the following story. A student refused to parrot
back what he had been taught in class. When the student protested, I was
asked to act as arbiter between the student and his professor.

I went to my colleague's office and read the examination question: 'Show
how it is possible to determine the height of a tall building with the aid
of a barometer.'

The student had answered: 'Take the barometer to the top of the building,
attach a long rope to it, lower the barometer to the street and then bring
it up, measuring the length of the rope. The length of the rope is the
height of the building.'

A high grade is supposed to certify competence in physics, but the answer
did not confirm this. I suggested that the student have another try at
answering the question. I gave the student six minutes, with the warning
that his answer should show some knowledge of physics. In the next minute
he dashed off his answer, which read: 'Take the barometer to the top of the
building and lean over the edge of the roof. Drop the barometer, timing its
fall with a stopwatch. Then, using the formula S = 1/2at2, calculate the
height of the building.'

At this point, I asked my colleague if he would give up. He conceded, and I
gave the student almost full credit.

In leaving my colleague's office, I recalled that the student had said he
had other answers to the problem, so I asked him what they were.

'Oh, yes. There are many ways of getting the height of a tall building with
the aid of a barometer. For example, you could take the barometer out on a
sunny day and measure the height of the barometer, the length of its
shadow, and the length of the shadow of the building, and by the use of a
simple proportion, determine the height of the building.'

Fine, I said. And the others?

'Yes. Take the barometer and begin to walk up the stairs. As you climb the
stairs, you mark off the length of the barometer along the wall. You then
count the number of marks, and this will give you the height of the
building in barometer units. A very direct method.'

'Finally, there are many other ways of solving the problem. Probably not
the best is to take the barometer to the basement and knock on the
superintendent's door. When the superintendent answers, you speak to him as
follows: "Mr. Superintendent, here I have a fine barometer. If you will
tell me the height of this building, I will give you this barometer".' 


Richard    :-)



-- 
Richard Carels,  University of Amsterdam      
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