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#174584 - 07/04/06 07:40 PM Re: Trapezoid. [Re: Achilles]
man_mind Offline
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Registered: 01/29/05
Posts: 957
I also never noticed that!

Very nifty.

It would actually explain why I do find it very attractive to look at, despite it not being my number 1 favorite color. While others I've had look at a post someone made, get unnerved, exiting the room quickly.

Ha! That is fascinating.
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#174585 - 11/04/06 03:38 PM Re: Law of the Trapezoid. [Re: melektaus8]
redheadgrl Offline


Registered: 09/24/06
Posts: 273
I read about the law of the trapezoid (The Devil's Notebook pg. 113) and was questioning why the trapezoid shape is disturbing. I don't find it disturbing at all, quite the opposite, and I have a number of trapezoid shapes in my home.

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#174586 - 11/04/06 04:36 PM Re: Law of the Trapezoid. [Re: redheadgrl]
Unknown Offline
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Registered: 03/31/05
Posts: 1649
It's effects are not always upon a conscious level but rather an emotional one.
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#174587 - 11/05/06 01:06 AM Re: Law of the Trapezoid. [Re: melektaus8]
TheAbysmal Offline


Registered: 09/22/06
Posts: 1019

Irrespective of any significance this contribution may have in the topic, I just started reading Ian Stewart's Concepts of Modern Mathematics today, and in reading it, a trapezoid sorta took center stage in My mind while reading the second chapter, Motion Without Movement. The second chapter starts with a treament of Euclid's proof of isosceles triangles, which--put very, very simply--is if you can flip the triangle over and it fits perfectly within the bounds of its original trace, it is isosceles. The problem with Euclid's proof, according to Zeno's paradoxes, is the concept of motion involved in it. Among Zeno's paradoxes, one stipulates that apparent motion, which we see everyday, cannot occur: To reach point B from point A, you must first pass through the midpoint C. To reach midpoint C from point A, you must first pass through midpoint D, and so on. Obviously, motion occurs, and so it should not overturn Euclid's proof, so a different view of motion must prevail. Closer to the trapezoid I come...

Transformations make Euclid's proof possible, specifically, transformations confined to rigid motion. For instance, give a rectangle with vertices between points (1,1), (1,3), (3,1), and (3,3) on a Cartesian coordinate system, and given the transformation J(x,y) = (x+1,y+1), it is easy to see the same rectangle has moved up and to the right by one coordinate. This is an example of translation. The other two types of rigid motion are reflection and rotation. Now, how about an example of unrigid motion.

Given the same rectangle and the transformation K(x,y) = (x2,xy), you see the same rectangle, but distorted, as if it were stretched around the left side of a soda can from a three-quarter perspective.

Here is where the trapzoid kicked in for Me. Can the trapezoid be some kind of transformation of the rectangle? I am a bit rusty on my geometry and trig, and I have been unable to think of a way to do it all day. It bugged Me so much from the moment I began mulling it over in My head that I had to put the book down.

Can any of you think of a transformation of the rectangle that results in a trapezoid?

Hail Satan!

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#174588 - 11/05/06 04:28 AM Re: Law of the Trapezoid. [Re: TheAbysmal]
Drimlybunk Offline
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Registered: 04/01/05
Posts: 928
Loc: California
J(x,y)=(xy,y)

Where the rectangle exists only in quadrants I and II.


Edited by Drimlybunk (11/05/06 04:33 AM)
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#174589 - 11/05/06 02:37 PM Re: Law of the Trapezoid. [Re: TheAbysmal]
Chess Offline
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Registered: 09/09/02
Posts: 1473
Loc: Chicago, IL USA
Quote:

I just started reading Ian Stewart's Concepts of Modern Mathematics today




Does it get into non-Euclidian realms? (That is, drop Euclid's "ugly" fifth postulate and see where you end up.) If so (and if you've got the math to approach the subject at least somewhat deeply), prepare to have your mind blown.

Quote:

The problem with Euclid's proof, according to Zeno's paradoxes, is the concept of motion involved in it. Among Zeno's paradoxes, one stipulates that apparent motion, which we see everyday, cannot occur: To reach point B from point A, you must first pass through the midpoint C. To reach midpoint C from point A, you must first pass through midpoint D, and so on. Obviously, motion occurs, and so it should not overturn Euclid's proof, so a different view of motion must prevail. Closer to the trapezoid I come...




The resolution to Zeno's Achilles and the Tortoise paradox is that it turns out an infinite series can add up to a finite sum. Thus the paradox is not a valid objection except in realms where calculus does not apply.

-Chess

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#174590 - 11/06/06 12:19 AM Re: Law of the Trapezoid. [Re: Chess]
TheAbysmal Offline


Registered: 09/22/06
Posts: 1019

Your observation of infinite series adding up to finite sums is indeed correct. I probably should have avoided mentioning Xeno's Paradoxes without also mentioning those only rendered Euclid's Proof of the Isosceles Triangle incorrect in his time; likewise, the author offers this bit of information in his book. I neglected to include it in My original post in a rush to get to the meat and potatos of it, the Trapezoid.

Interestingly enough, Drimlybunk shows how thinking inside the box, the first and second boxes, offers a partial solution. Here is where I walk the fine line between compulsion and indulgence. :) Perhaps there is a significance to this I may later discover...

The subject of math, in all its flavors, has never failed to blow My mind. I enjoy it much, even what of it I may never apply beyond entertainment. What I find so intriguing about Concepts of Modern Mathematics is that it is more of an exposé of understanding math and its beauty, rather than blind manipulation of proofs and numbers. The author really, deeply loves the subject, and you can tell it from the prologue alone.

Hail Satan!

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#174591 - 11/07/06 11:00 AM Re: Law of the Trapezoid. [Re: redheadgrl]
Bill_M Offline
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Registered: 07/28/01
Posts: 11532
Loc: New England, USA
Quote:

I read about the law of the trapezoid (The Devil's Notebook pg. 113) and was questioning why the trapezoid shape is disturbing. I don't find it disturbing at all, quite the opposite, and I have a number of trapezoid shapes in my home.




The geometric figure shown in the book actually has a line of symmetry. That in fact makes it look like a somewhat "balanced" shape. But when you take a more general look at what a trapezoid is (a quadrilateral with only two sides parallel) you can see in manifested in some "uneasy"-looking geometry in the 3D world. A perfect example that LaVey gives is a room where the walls, ceiling, and/or floor do not meet at perfect 90-degree angles. He confirmed that this showed up in the kind of rooms where people would get the creeps without knowing why.

Experiments have shown time and time again that humans like to see symmetry. Lack of symmetry makes us feel uneasy. But when you make things more and more asymmetric, it can get to a point where shapes just look messy and don't move the observer's mind. Trapezoids tend to have just enough parallel lines or symmetry to make us "want" to "complete" the symmetry in our minds, but the non-parallel lines keep irking the mind at the same time. This is what can cause uneasy-looking geometry.

The Law of the Trapezoid though isn't limited to offering psychological explanations for allegedly haunted place, though. It has its applications. Sometimes we need asymmetry to help us "think outside of the box" too. For example, I think the traditional Satanic altar has a nice lack of symmetry by placing only one white candle to the right.
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#174592 - 11/07/06 11:04 AM Re: Law of the Trapezoid. [Re: TheAbysmal]
Bill_M Offline
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Registered: 07/28/01
Posts: 11532
Loc: New England, USA
Quote:

The subject of math, in all its flavors, has never failed to blow My mind.




Mathematics is one of my own passions, that's for sure. I definitely want to check out the volume you mentioned.

My own personal view of the trapezoid is that it's the simplest way to represent pushing things into the next "dimension". If you hold up a square sheet of paper in front of you, then start to tilt the top back, it will look trapezoidal because of your perspective; the top will look shorter than the bottom because it's further away. Likewise in the ritual chamber we suspend disbelief in order to "push" things in an unconventional "direction".
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#174593 - 11/07/06 11:33 AM Re: Law of the Trapezoid. [Re: Enchantress]
tovasshi Offline


Registered: 02/16/05
Posts: 1414
Loc: Banana, Canada
My English classroom is a blue trapezoid. The walls art is large wood trapezoids. The building in wich it resides has trapezoid office areas for the staff members.

My highest grade is in that class.
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#174594 - 11/07/06 01:22 PM Re: Law of the Trapezoid. [Re: Bill_M]
Drimlybunk Offline
CoS Member

Registered: 04/01/05
Posts: 928
Loc: California
Quote:

If you hold up a square sheet of paper in front of you, then start to tilt the top back, it will look trapezoidal because of your perspective;




I find this transformation much more suited to answer TheAbysmal's question than my own. Although mathematically it would only result in a flatter rectanlge, it's magical and pragmatic implications are far superior.

(I'm much more a fan of art than math... though I do enjoy both.)

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#174595 - 11/09/06 08:28 AM Re: Law of the Trapezoid. [Re: Drimlybunk]
tekku Offline
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Registered: 07/24/06
Posts: 1261
Loc: Behind You
I have been watching this topic for some time and have really enjoyed the information conveyed about different aspects of what makes up The Law of the Trapezoid and its effects.

I would just like to ask, aside from the mentioned texts and theories discussed in this thread and also aside from The Devils Notebook.

What other texts and/or theories would be recommended reading as I would really like to study this subject further.
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#174596 - 11/09/06 11:08 AM Re: Law of the Trapezoid. [Re: Bill_M]
Mr_47 Offline
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Registered: 05/22/06
Posts: 3082
Loc: Pure Imagination
I was waiting for our resident mathematician to put in his two cents on this one.

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#174597 - 11/10/06 09:40 PM Re: Law of the Trapezoid. [Re: melektaus8]
PeachesPartridge Offline


Registered: 10/11/06
Posts: 68
Loc: where the youngsters get hyphy...
A friend and I recently created this structure, to be used as a temporary art gallery:


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#174598 - 11/10/06 11:30 PM Re: Law of the Trapezoid. [Re: PeachesPartridge]
Enchantress Offline

CoS Member

Registered: 02/11/05
Posts: 2166
Loc: Canada
Excellent endeavour! Have you created other structures such as this? It would also look great if you added a fog machine to it.
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