n-Curving - Curve Transformation.

Slide 1 : 1 n-Curving A Method of Creating Beautiful Mathematical Curves References: Sebastian Vattamattam & R. Sivaramakrishnan, “A Note on Convolution Algebras”, Chapter 6, Recent Trends in Mathematical Analysis, Allied Publishers, 2003 http://en.wikipedia.org/wiki/Functional-theoretic_algebra Based on Functional Theoretic Algebras

Slide 2 : 2/1/2010 2 Basic Definitions

Slide 3 : 2/1/2010 3 Examples of Closed Curves

Slide 4 : 2/1/2010 4 Examples of Closed Curves(Loops) 0 1

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Slide 12 : 2/1/2010 12 Functional Theoretic Algebra In a nutshell

Slide 13 : 2/1/2010 13 Ref: Sebastian Vattamattam, “Non-Commutative Function Algebras”, Bulletin of Kerala Mathematics Association, Vol. 4, No. 2(2007 December)

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Slide 15 : 2/1/2010 15 Examples of Open Curves

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Slide 21 : 2/1/2010 21 n-Curving ? Ref: Sebastian Vattamattam, Transforming Curves by n-Curving, Bulletin of Kerala Mathematics Association, Vol. 5, No.1(2008 December)

Slide 22 : 2/1/2010 22 N-Curving the Line Segment l

Slide 23 : 2/1/2010 23 Unit Circle – Line Segment

Slide 24 : 2/1/2010 24 N-Curving the Line Segment l

Slide 25 : 2/1/2010 25 Cardioid – Line Segment

Slide 26 : 2/1/2010 26 N-Curving the Line Segment l

Slide 27 : 2/1/2010 27 Rhodonea-Cos2 – Line Segment

Slide 28 : 2/1/2010 28 N-Curving the Line Segment l

Slide 29 : 2/1/2010 29 Rhodonea-Cos3 – Line Segment n = 1 n = 2 n = 3 n = 10

Slide 30 : 2/1/2010 30 N-Curving the Line Segment l

Slide 31 : 2/1/2010 31 RhodoneaSin2 – LineSegment

Slide 32 : 2/1/2010 32 N-Curving the Line Segment l

Slide 33 : 2/1/2010 33 DoubleFolium – LineSegment n = 1 n = 2 n = 3 n = 4

Slide 34 : 2/1/2010 34 N-Curving the Line Segment l

Slide 35 : 2/1/2010 35 Limacon– LineSegment

Slide 36 : 2/1/2010 36 Random Examples

Slide 37 : Example 1 n-Curved Cosine with Rhodonea-cos2 2/1/2010 37

Slide 38 : 2/1/2010 38 Example 2 n-Curved Cosine with Double Folium

Slide 39 : 2/1/2010 39 Example 3 n-Curved Archimedean Spiral with Unit Circle

Slide 40 : 2/1/2010 40 Example 4 n-Curved Archimedean Spiral with Cardioid

Slide 41 : 2/1/2010 41 The Class Ends Not in your mind Thank You

Slide 42 : 2/1/2010 42 Quit Not Before You Type Your Comments