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:

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

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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...

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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?

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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:

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to dist :location

op sqrt sum(xcor-first :location)*(xcor-first :location)~

(ycor- last :location)*(ycor- last :location)

end

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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]]

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