vectors &laquo; WordPress.com Tag Feed http://en.wordpress.com/tag/vectors/ Feed of posts on WordPress.com tagged "vectors" Sun, 29 Nov 2009 18:34:51 +0000 http://en.wordpress.com/tags/ en <![CDATA[VECTOR: LITTLE CATS SILHOUETTE]]> http://bibidesigner.wordpress.com/2009/11/27/vector-little-cats-silhouette/ Fri, 27 Nov 2009 15:55:08 +0000 bibidesigner http://bibidesigner.wordpress.com/2009/11/27/vector-little-cats-silhouette/

Silhuetas de Gatos. Vetor: Corel Draw

]]> <![CDATA[Intuitive Circular Reasoning]]> http://vikramsundar.wordpress.com/2009/11/24/intuitive-circular-reasoning/ Wed, 25 Nov 2009 05:45:57 +0000 vikramsundar http://vikramsundar.wordpress.com/2009/11/24/intuitive-circular-reasoning/

In mathematical proofs, circular reasoning is a deadly sin; in short, to prove A, you assume A, prove B using A, and then prove A using B. In short, you have assumed A to prove A, but this tells you nothing… so there is no result. Circular reasoning usually results from a long proof in which you make a mistake; it is not as obvious as the above example. However, intuitive circular reasoning is very common; in fact, a large portion of mathematics was developed in this fashion and worked this way.

I will define intuitive circular reasoning as follows: I take an intuitive definition of A (that is, not rigorous in any fashion), then define B in a way that satisfies my intuitive definition of A, then define A rigorously that satisfies my new definition of B. I can generalize this: I use some desirable property B of an intuitive definition A to rigorously define A. This may seem strange, illogical, and completely unnecessary – but let me show some examples.

We define a tangent to a circle as a line which touches the circle at one point. But what is a tangent line to a function? You may say “a line that touches the function at one point” but take this example: Find the tangent line to f(x) = cos x when x = 0. The answer is obviously y = 1 (by differential calculus), but y = 1 touches the function at infinitely many points. You may try to use the derivative, but the derivative is the slope of the tangent line; this is circular reasoning (non-intuitive). So we have this picture in our minds and an intuitive definition of a tangent line. Using this and some elementary geometry we can easily prove that the derivative of a function f(x) at x = a, f’(a), is the limit as h approaches zero of f(x+h)-f(x)/h. Then, we can rigorously define the derivative f’(x) as the above stated limit and the tangent line as the line that intersects a function at the point x = a and has slope f’(a). Is this circular reasoning? The answer is yes and no. Yes, this is intuitive circular reasoning, but circular reasoning revolves around rigor. Recall that our first definition of the tangent line was intuitive; as a result, the second definition is the rigorous definition. In rigorous proofs, we would start with the definition of a derivative, then of a tangent line, and then show the pictorial qualities that accompany our intuitive definition. This order is rigorous and avoids circular reasoning; yet we came up with this proof through what can be considered circular reasoning; this is intuitive circular reasoning.

Let us take a look at area. The area of a triangle is bh/2, rectangle lw, parallelogram bh, trapezoid b(h_1+h_2)/2, rhombus d_1d_2/2, circle πr^2, etc. What about the area under the function t^3 from 0 to x above the t-axis (without integrals)? We cannot define it (recall that my previous blog entry on FTC did not rigorously define area; it was not meant to be intuitive). But we have an intuitive idea, and using this we determine Riemann sums, the definition of a definite integral, and FTC. After this work, we can define area based on FTC and the definition of a definite integral. Once again, we have circular reasoning.

Notice that my above examples have related primarily to the first definition; not the generalization. I will now give an example that is based on the generalization. Take multiplication of matrices. Recall that a matrix is based on transforming vectors; in addition, a matrix multiplied by a vector is another vector. If we compose transformations, the associative property SHOULD hold. This, along with some algebra, leads to our current definition of multiplication of matrices. This rigorous definition is given in all PreCalculus books, unfortunately without any explanation. The beauty behind it is obscured, but it comes through the process of intuitive circular reasoning.

There are many other examples of intuitive circular reasoning; here I have listed a few. Nevertheless, this idea has been instrumental in the development of mathematics through the ages.

]]> <![CDATA[فيكتور]]> http://ssdaa.wordpress.com/2009/11/22/%d9%81%d9%8a%d9%83%d8%aa%d9%88%d8%b1/ Sun, 22 Nov 2009 06:25:20 +0000 ssdaa http://ssdaa.wordpress.com/2009/11/22/%d9%81%d9%8a%d9%83%d8%aa%d9%88%d8%b1/

قسم كامل للفيكتور vector  منوع وشامل مجموعه كبيره ومتجدده دائما والتحميل كالعاده مباشر من على صور صدى

تجدونها هنا

فيكتور

vectord

]]> <![CDATA[Sta. Catrina de los tenis colgados]]> http://cyanalcien.wordpress.com/2009/11/14/sta-catrina-de-los-tenis-colgados/ Fri, 13 Nov 2009 20:00:04 +0000 cyanalcien http://cyanalcien.wordpress.com/2009/11/14/sta-catrina-de-los-tenis-colgados/

Personaje que desarrolle para un concurso (Calaveras Edumac, no gane pero me la pase bien jejeje, ni modo, para eso son los concursos para participar y pasársela bien). Así que aquí esta. Con este trabajo me dieron más ganas como de customizar algo, o decorar una pared… Ojalá alguíen se anime y me invite a customizar alguna cosa. Ahí si saben de alguna convocatoria o algo avísenme!!!

4084295395_61c77a71e9

]]> <![CDATA[Vector Addition]]> http://physi.wordpress.com/2009/11/12/vector-addition/ Thu, 12 Nov 2009 21:35:57 +0000 Mr A http://physi.wordpress.com/2009/11/12/vector-addition/

Vector Addition Flash Applet, created by PhET.

]]> <![CDATA[Vector - Sanzen'in Nagi]]> http://awesmoe.wordpress.com/2009/11/09/vector-sanzenin-nagi/ Sun, 08 Nov 2009 22:47:19 +0000 Shini http://awesmoe.wordpress.com/2009/11/09/vector-sanzenin-nagi/ <![CDATA[Free Vector Art Download Free Vector Graphics and Vector Art at http://graphics.lk]]> http://eduliver.wordpress.com/2009/11/06/free-vector-art-download-free-vector-graphics-and-vector-art-at-httpgraphics-lk/ Fri, 06 Nov 2009 17:09:49 +0000 ireshanas http://eduliver.wordpress.com/2009/11/06/free-vector-art-download-free-vector-graphics-and-vector-art-at-httpgraphics-lk/

graphics.lk is an index of Free Vector Graphics available for download by some of the best designers around the world

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]]> <![CDATA[Free Vecto Arts]]> http://eduliver.wordpress.com/2009/11/06/free-vecto-arts/ Fri, 06 Nov 2009 16:55:05 +0000 ireshanas http://eduliver.wordpress.com/2009/11/06/free-vecto-arts/

http://graphics.lk
Visit Our Main Site And Downloading Free Vector Arts

]]> <![CDATA[Brands of the World – 82.000 Vector Logo DVD]]> http://gfxforyou.wordpress.com/2009/11/04/brands-of-the-world-%e2%80%93-82-000-vector-logo-dvd/ Wed, 04 Nov 2009 12:09:00 +0000 artlinks2008 http://gfxforyou.wordpress.com/2009/11/04/brands-of-the-world-%e2%80%93-82-000-vector-logo-dvd/

brandsoft-vector-logos-reupload

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]]> <![CDATA[New Topics in Vectors Homework Help & Assignment Help]]> http://hunt99.wordpress.com/2009/11/04/new-topics-in-vectors-homework-help-assignment-help/ Wed, 04 Nov 2009 06:40:16 +0000 hunt99 http://hunt99.wordpress.com/2009/11/04/new-topics-in-vectors-homework-help-assignment-help/

Find Some new Topics in Vectors:

 

]]> <![CDATA[Illustration 11 - Little One]]> http://drutest.wordpress.com/2009/11/03/illustration-11-little-one/ Tue, 03 Nov 2009 18:00:27 +0000 drutest http://drutest.wordpress.com/2009/11/03/illustration-11-little-one/

Print

 

]]> <![CDATA[Relative Motion Homework]]> http://timlangford.wordpress.com/2009/11/03/relative-motion-homework/ Tue, 03 Nov 2009 01:20:23 +0000 timlangford http://timlangford.wordpress.com/2009/11/03/relative-motion-homework/

Do p.57 #1-4.  Note that in airplane problems:

- ”air speed” really means “air velocity”, that is, velocity of the body (the airplane) relative to the medium (the air). 

-  ”wind speed” really means “wind velocity”, that is, velocity of the medium (the air) relative to the Earth. 

- “ground speed” really means “ground velocity”, that is, velocity of the body (the airplane) relative to the Earth.

]]> <![CDATA[Illustration 9]]> http://drutest.wordpress.com/2009/11/02/illustration-9/ Mon, 02 Nov 2009 21:50:21 +0000 drutest http://drutest.wordpress.com/2009/11/02/illustration-9/

Illustration 9

]]> <![CDATA[Illustration 8]]> http://drutest.wordpress.com/2009/11/02/illustration-8/ Mon, 02 Nov 2009 21:47:13 +0000 drutest http://drutest.wordpress.com/2009/11/02/illustration-8/

Illustration 9

]]> <![CDATA[Illustration 7]]> http://drutest.wordpress.com/2009/11/02/illustration-7/ Mon, 02 Nov 2009 21:45:28 +0000 drutest http://drutest.wordpress.com/2009/11/02/illustration-7/

Illustration 7

]]> <![CDATA[Illustration 6]]> http://drutest.wordpress.com/2009/11/02/illustration-6/ Mon, 02 Nov 2009 18:43:55 +0000 drutest http://drutest.wordpress.com/2009/11/02/illustration-6/

Illustration 6

]]> <![CDATA[Illustration 5]]> http://drutest.wordpress.com/2009/11/02/illustration-5/ Mon, 02 Nov 2009 18:27:06 +0000 drutest http://drutest.wordpress.com/2009/11/02/illustration-5/

portfolio33

]]> <![CDATA[Illustration 4]]> http://drutest.wordpress.com/2009/11/02/illustration-4/ Mon, 02 Nov 2009 18:26:05 +0000 drutest http://drutest.wordpress.com/2009/11/02/illustration-4/

Print

 

]]> <![CDATA[Illustration 3]]> http://drutest.wordpress.com/2009/11/02/illustration-3/ Mon, 02 Nov 2009 18:08:51 +0000 drutest http://drutest.wordpress.com/2009/11/02/illustration-3/

portfolio18

]]> <![CDATA[Illustration 2]]> http://drutest.wordpress.com/2009/11/02/illustration/ Mon, 02 Nov 2009 16:53:01 +0000 drutest http://drutest.wordpress.com/2009/11/02/illustration/

Draw me out to the ball game

]]> <![CDATA[ARIDI Vol1-37 (Full)]]> http://gfxforyou.wordpress.com/2009/10/31/aridi-vol1-37-full/ Sat, 31 Oct 2009 04:36:02 +0000 artlinks2008 http://gfxforyou.wordpress.com/2009/10/31/aridi-vol1-37-full/

ARIDI Vol1-37 (Full)

ARIDI Vol1-37 (Full) (1 DVD)

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