Equation of Egg Shaped Curve

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2022-05-12 07:00:14

When we search for the internet about an oval curve, several sites of Egg Curves and Ovals, Oval and Cassini oval are found. But there seem to be little equations of a curve near a real egg shape. So, an equation of egg shaped curve which resembles closely to the shape of a chicken egg is pursued here apart from a mathematical definition of "oval curve". This starts from the short article that Yamamoto has published in Library Newsletter No. 63 (2006) of Ibaraki National College of Technology. Succedingly, "Equation of Egg Shaped Curve of the Actual Egg is Found" is released in this page on Apr. 27, 2007, "Equation of Egg Shaped Curve II (Egg Shaped Curve I proposed by Mr. Itou" is released on Mar. 29, 2008, "Equation of Egg Shaped Curve III (Egg Shaped Curve I proposed by Mr. Asai)" is released on Aug. 02, 2009, "Equation of Egg Shaped Curve IV (Egg Shaped Curve II proposed by Mr. Asai)" is released on Sep. 18, 2009, "Equation of Egg Shaped Curve V" is released on Nov. 08, 2009, "Equation of Egg Shaped Curve VI" is released on Nov. 26, 2009, and "Egg Shaped Curve VII (Egg Shaped Curve III proposed by Mr. Asai)" is released on May. 29, 2011. For a while after these, there was no publication of an oval curve close to the shape of a real chicken egg. However, as of March 2020, "Equation to fit an egg", "HÜGELSCHÄFFER EGG". "Egg Curve", "Egg-curve", "Let's display an egg curve" and "The Python Egg Curve" have been issued. Afterwards, this site is introduced in How can I find the surface area of a normal chicken egg? , How to place random points on an egg? , The room of Jukchou , 271828_slide_Log , WolframAlpha Computational Intelligence , draw egg curves from an equation , Egg quations , Creating a 3D ellipsoid from a 2D ellipse , Egg Curves and Ovals [ Eilinien und Ovale in German ] , Eilinien und Ovale , Two-dimensional Yamamoto (2017)'s Egg Curve GENERATING AVIAN EGG USING RATIONAL BEZIER QUADRATIC CURVES , Creating a 3D Egg in SketchUp with U-V PolyGen , If anyone knows the equation of the egg curve, please let me know! , Graphs of Eggs , Negative Volume of Revolution? , How do you find the surface area of an egg using calculus? , etc., and this site is also cited in papers such as Predictive Calculation Model of Vehicle Cabin Temperature in Environmental Laboratory and Comparison with Cooling Experiment , An Egg Volume Measurement System Based on the Microsoft Kinect , "DSEG": Original 7-segment and 14-segment fonts 5.Misc , "DSEG": Original 7-segment and 14-segment fonts , Distributed mesh generation for objects with shape variability , Negative Volume of Revolution? , Projecting Cartesian Coordinates onto the Surface of an Egg in Egg-bot Coordinates , Distributed mesh generation for objects with shape variability , Packing Ovals In Optimized Regular Polygons , KONSTRUKSI PERSAMAAN PERMUKAAN BENTUK-TELUR MENGGUNAKAN KURVA BENTUK-TELUR HUGELSCHAFFER , A Modified Avian Egg Shaped CPW Fed Printed Monopole for SWB Applications , Membrane-Wrapping Contributions to Malaria Parasite Invasion of the Human Erythrocyte , طراحي مفهومي و بهينهسازي کشتي هوايي ارتفاع باال بهوسيلة الگوريتم ژنتيک (Persian) (Conceptual design and optimization of high altitude aircraft by genetic algorithm) , Fun With SAS ODS Graphics: Easter Egg Equation Hunt , KONSTRUKSI PERSAMAAN PERMUKAAN BENTUK-TELUR MENGGUNAKAN KURVA BENTUK-TELUR HUGELSCHAEFER (Indonesian) ( CONSTRUCTION OF EGG-SHAPE SURFACE EQUATIONS USING HUGELSCHAEFER'S EGG-SHAPE CURVE) , MATHEMATICS IA -- Mathematical investigation of an egg , Regulatory Mechanisms in Biosystems -- Mathematical interpretation of artificial ovoids and avian egg shapes (part I) , etc. Also, this site was also introduced in the blog of What is mathematical equation for an egg? (Archive version) , though this article in its blog is gone now. As seen by looking at each site or treatise, the author's name written in it is "Nobuo Yamamoto", "N. Yamamoto" or "Yamamoto N.". On the otherhand, the address of this site has passed "Http://www16.ocn.ne.jp/~akiko-y/Egg/index_egg.html", "http://www.geocities.jp/nyjp07/Egg/index_egg.html", "http://www.geocities.jp/nyjp07/index_egg.html", and becomes the current "http://nyjp07.com/index_egg.html". We can't use the old address, but searching for old addresses with a free Internet Archive search may reveal the site at the time it was saved.

An equation of egg shaped curve (egg curve), which resembles to the shape of the actual egg more than Cassini oval etc. (continuing from the left), is obtained below. In the x-y coordinate shown in Fig 1, there is some point Q on the -axis, and there is the given segment PQ. The point Q is supposed to move on the -axis co-sinusoidally according to the angle of the segment PQ as the following; . (1) In the same time, the length of the segment PQ is supposed to vary co-sinusoidally as follows; , (2) where . (3) In such a way, the trajectory of the point P is tried to be found to become an egg shaped curve. In Fig.1, the point P is expressed as , (4) and . (5) It is unexpectedly difficult to solve the above equations. Then, if we solve the equations from (1) to (5) under the assumption given in the following; , (6) we obtain as the fourth-order relation that . (7)