April 19, 2023

CURVE STITCHINGBy

-Gauri VarmaIX B

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Introduction

Curve stitching is a form of string art where smooth curves are created through the use of straight lines. Curve stitching is a craft in which a series of geometric forms are used to create the appearance of a curve. While curved stitched designs appear to have complex, graceful curves and a three dimensional aspect, they are actually totally flat, and comprised entirely of straight lines.

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History

English mathematician Mary Everest Boole is generally given the credit for inventing curve stitching. She developed the technique in the early 1900s as an aid for teachers who wanted an interactive method for introducing children to geometry. Curve stitching continues to be used for this purpose, in addition to being popular with some crafters.

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Basic Construction

A geometric shape is drawn on the stitching surface, and then a needle and thread are used to create a series of straight lines running back and forth from one side of the shape to the other. Each side of the shape is pierced several times with the thread, creating a series of connections between it and a neighboring side. As the lines intersect, the suggestion of a curve is created at the intersections of the line, with the curve appearing more realistic the more lines there are.

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Parabola

A parabola is a curve where any point is at an equal distance from:

a fixed point (the focus), and a fixed straight line (the directrix)Reflector PropertyA parabola has this amazing property: Any ray parallel to the axis of

symmetry gets reflected off the surface straight to the focus.

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Uses of Parabolae in Real Life

Uses of a Parabola satellite dishes, radar dishes, concentrating the sun's rays to make a

hot spot, the reflector on spotlights and torches, They are used for math and science.

They are used in flashlights, solar cooking, throwing or kicking a ball, suspension bridges, and diving.

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Parabola Quadrilateral A parabola

quadrilateral is a normal quadrilateral in which the angles have been used to make a parabola. With this as a base, angles of cubes and cuboids are also used to make parabolae which form beautiful and intricate designs.

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3-Dimensional Star

If you use the lines that connect up the center of a regular polygon to each of the sides, you get star figures made out of your parabolas.

The process of creating parabolic sections can be done with any angle and you can use angles that make polygons and use the process on all of the sides. Here I have used a pentagon as the base and constructed a 3-D star using the process of constructing parabolas.

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Ellipse

An ellipse is the set of all points on a plane whose distance from two fixed points F and G add up to a constant. An ellipse usually looks like a squashed circle. It is defined by two special points called foci. ‘F’ is a focus and ‘G’ is a focus so together they are called foci. Ellipse is a conic section (a section of a cone). 

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Uses of an EllipseThe ellipse also has the reflective

property which has been useful in medicine, to create a machine to destroy kidney stones and gallstones called a lithotripter. It uses shockwaves to crush kidney stones into tiny pieces that are easier for the body to dispose of. This is a very useful and important application of the reflective property of an ellipse.

"The Whisper Chamber" at the United States capital is another example. Stand at one focus and you can perfectly hear someone whispering at the other focus, though it is much too far away to hear.

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Concentric circlesConcentric circles are

also mainly used as designs and for decoration. They can be very intricately designed and are sometimes so very complicate that they can’t be remade or traced back to the first step. They are indeed very beautiful masterpieces of curve stitching.

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Heart

A heart is made with combinations of different types of curve stitching designs. It is a combination of a cardioid, an ellipse and a concentric circle. This design may not exactly look like a heart but is the closest design possible to a heart. It can also be more intricate and closer to the shape of a heart but can be done with the help of a computer.

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Conclusion

From this project, I have explored deeply into the geometric world and learned how interesting and fun it can be. This assignment has helped me gain a lot of interest in the geometric field of mathematics and learn a lot about the use of it in real life. I profusely thank all who have helped me in this project and hope to receive many more works like this.