LOGO-L> Off-computer -- on to Logo 
Author Message
 LOGO-L> Off-computer -- on to Logo

Here are two different problems:

1.  Given a line that you want to EXTEND to make
    a Golden Section.

2.  Given a line that you want to DIVIDE into
    a Golden Section.

Granted, once you know the magic number (approximately)
1.6180339887499, you can just calculate it.

However, there are geometric constructions to solve
each of these problems.

One construction was found in a dictionary illustration
of the Golden Section (and later in the book titled
"Fascinating Fibonaccis").

The other was found in a Wentworth geometry text
originally copyrighted in 1888.

This was an off-computer exploration but a turtle
graphics drawing can be made to visually verify
that both constructions define the same ratio.

By the way, did you know there is such a thing as
a Golden Triangle?

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





Mon, 18 Mar 2002 03:00:00 GMT  
 LOGO-L> Off-computer -- on to Logo
Can you make a 3-side die?

(Not a simulation, but a physical object that you
can hold in your hand.)

This off-computer exploration lead to using Logo
to draw the patterns for the panels used to build
models.

It was easily extended to make a 2-sided die that
was not a coin, a 4-sided die that was not a
tetrahedron, and a 6-sided die that was not a cube.

Not that it's useful, but what would you use for
a 1-sided die (aside from a Mobius strip)?
---------------------------------------------------------------





Mon, 18 Mar 2002 03:00:00 GMT  
 LOGO-L> Off-computer -- on to Logo

Quote:

> Can you make a 3-side die?

Sure, easy
Take a triangular shaped pencil-like thing, sharpen both ends, and throw
it, the down side is it
(Unless you stick it in the ceiling :-> )

(I think a football has 4 pieces of leather (make one with n pieces for
an n sided die)

Quote:

> (Not a simulation, but a physical object that you
> can hold in your hand.)

> This off-computer exploration lead to using Logo
> to draw the patterns for the panels used to build
> models.

> It was easily extended to make a 2-sided die that
> was not a coin, a 4-sided die that was not a
> tetrahedron, and a 6-sided die that was not a cube.

> Not that it's useful, but what would you use for
> a 1-sided die (aside from a Mobius strip)?
> ---------------------------------------------------------------




--
 ...wex


Tue, 19 Mar 2002 03:00:00 GMT  
 LOGO-L> Off-computer -- on to Logo
Oh, and how about a volleyball for a 1 sided die?
(anypoint on the outside is 1 - can't land on the inside (analogue to a
coin on edge, doesn't count))

Quote:

> Here are two different problems:

> 1.  Given a line that you want to EXTEND to make
>     a Golden Section.

> 2.  Given a line that you want to DIVIDE into
>     a Golden Section.

> Granted, once you know the magic number (approximately)
> 1.6180339887499, you can just calculate it.

> However, there are geometric constructions to solve
> each of these problems.

> One construction was found in a dictionary illustration
> of the Golden Section (and later in the book titled
> "Fascinating Fibonaccis").

> The other was found in a Wentworth geometry text
> originally copyrighted in 1888.

> This was an off-computer exploration but a turtle
> graphics drawing can be made to visually verify
> that both constructions define the same ratio.

> By the way, did you know there is such a thing as
> a Golden Triangle?

> ---------------------------------------------------------------




--
 ...wex


Tue, 19 Mar 2002 03:00:00 GMT  
 
 [ 4 post ] 

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