LOGO-L> DIST and Math 
Author Message
 LOGO-L> DIST and Math

Hello Turtlers,

Recently I proposed a class-activity (see: 4-sided polygons). I want to
propose here a family of activities, which suits students of various
math (mainly geometry) levels.

Here are 2 sample problems:

********************************************************************
1. In a square, how many times is the diagonal longer than its side?
********************************************************************

Clear the screen, it's very important that the turle begins from its
home. Draw a square with side(s) of 100:
        CS REPEAT 4[FD 100 RT 90]
Now we know that the coordinates of the point opposite the HOME is [100
100], so you say:
        PR DIST[100 100]
and Logo replies with 141.421... . That's 1.414 times longer than the
square's side.
(actually you don't need that drawing, it's done only for visualization
reasons).

Try it again with other squares, you always come to the same conclusion.

Result: The diagonal of a squre is 1.414 (more precisely - the square
root of 2) times the square;s side.
No need to use the Pythagorean Theorem nor the Geometric Supposer...

********************************************************************
2. Given a parallelogram with sides 50 and 100. The angles are 60 and
120 degs. What is the length of the longer diagonal of the
parallelogram?
********************************************************************

This time we can't readily know the coordinates of the needed vertex.
Again the turtle comes to our help:
        CS RT 30 REPEAT 2[FD 50 RT 60 FD 100 SHOW POS RT 120]
and Logo replies with [125 43.30127]
All you have now is to say:
        PR DIST[125 43.30127]
and you get the needed distance: 132.28...

(years later the student will learn, that this problem can be solved
mathematically by the Cosine Theorem).

If your Logo doesn't have DIST function, put the following in the
editor, before the intended activity:

=========================================================
to dist :location
op sqrt sum(xcor-first :location)*(xcor-first :location)~
           (ycor- last :location)*(ycor- last :location)
end
=========================================================

Many other such problems can be invented by the teacher to be solved
with Logo and DIST. Just remember to begin always at the turtle's home.

Enjoy,

[[Yehuda]]

---------------------------------------------------------------





Sun, 05 Mar 2000 03:00:00 GMT  
 LOGO-L> DIST and Math

Quote:
> Date:          Wed, 17 Sep 1997 13:16:16 +0200



> Subject:       LOGO-L> DIST and Math

> Hello Turtlers,

> Recently I proposed a class-activity (see: 4-sided polygons). I want to
> propose here a family of activities, which suits students of various
> math (mainly geometry) levels.

> Here are 2 sample problems:

> ********************************************************************
> 1. In a square, how many times is the diagonal longer than its side?
> ********************************************************************

[...]

Quote:
> ********************************************************************
> 2. Given a parallelogram with sides 50 and 100. The angles are 60 and
> 120 degs. What is the length of the longer diagonal of the
> parallelogram?
> ********************************************************************

[...]

Thank you Yehuda,

Nice idea. I'll try this activity soon with my 7th graders who have
just began to learn Geometry.

Regards,
Olga.

---------------------------------------------------------------





Sun, 05 Mar 2000 03:00:00 GMT  
 LOGO-L> DIST and Math

Quote:

> > Date:          Wed, 17 Sep 1997 13:16:16 +0200



> > Subject:       LOGO-L> DIST and Math

> > Hello Turtlers,

> > Recently I proposed a class-activity (see: 4-sided polygons). I want to
> > propose here a family of activities, which suits students of various
> > math (mainly geometry) levels.

> > Here are 2 sample problems:

> > ********************************************************************
> > 1. In a square, how many times is the diagonal longer than its side?
> > ********************************************************************

> [...]

> > ********************************************************************
> > 2. Given a parallelogram with sides 50 and 100. The angles are 60 and
> > 120 degs. What is the length of the longer diagonal of the
> > parallelogram?
> > ********************************************************************

> [...]

> Thank you Yehuda,

> Nice idea. I'll try this activity soon with my 7th graders who have
> just began to learn Geometry.

> Regards,
> Olga.

Olga Dear,

Good like, and let us know how was it, so we all can learn from it.

[[Yehuda]]

---------------------------------------------------------------





Sun, 05 Mar 2000 03:00:00 GMT  
 
 [ 3 post ] 

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