"All the Real Math To Which School (Including College) Refused Yo u Access."

[Bert Freudenberg]

Am Donnerstag, 17.04.03 um 21:24 Uhr schrieb Alan Kay:

> I think lots of insight can be gained by seeing what the "weighing 
> angles" illustration is all about.
>
> Notice that when the angle is 90? the scale will measure the full 
> weight of the dumbell and wheels. When the angle is 0?, the scale will 
> show zero weight. In between, the scale will show the weight of the 
> dumbell and wheels in the direction down the inclined plane. "Weight" 
> is actually defined as the mass of an object times the force of 
> gravity on it ( w = mg ).

If I were picking nits I'd point out that actually weight is a force 
(measured in Newtons), not gravity. Force is mass times acceleration 
(Newton's second law). So in this special case, weight is mass times 
gravitational *acceleration*. Weight is only another term for 
gravitational force. But you knew that ;-)

>  So what we are seeing on the scale is the differential effect of 
> gravity down inclined planes at different angles.
>
> If we use a protractor to tilt the inclined plane (say) every 5? then 
> we can write down the different forces down the plane. If we divide 
> these numbers by the maximum weight when the angle is 90, we will get 
> numbers between 0 and 1. These numbers can be put into a holder as a 
> table of values and used in a wide variety of projects, including 
> making a roller coaster. So there is no need to use the idea of "sine" 
> -- and this makes projects that need these ratios -- like roller 
> coasters -- much more in the range of 5-7th graders.

What do you think of measuring the forces in the Etoy itself (for 
example, by taking the vertical extent of a rotated line)? Of course, I 
can see the value of using real-world data. Do you think it's too large 
a step to "see" the height of the angle, which is proportional to the 
force?

-- Bert