Some of you are celebrating Easter this weekend and I thought I will make a short post for this event. So, I have searcher the great World Wide Web in search of some great designs for Easter eggs inspired from mathematics. Also, while I show you those images I will say a couple of words about ellipsoids (the mathematical shape of an egg and not only).
An ellipsoid is a closed quadric surface that is a three-dimensional analogue of an ellipse. Any planar cross section passing through the center of an ellipsoid forms an ellipse on its surface: this degenerates to a circle for sections normal to the symmetry axis of an ellipsoid of revolution (or all sections when the ellipsoid degenerates to a sphere.)
To do those great designs on eggs, we need to use spherical geometry. Spherical geometry is a type of non Euclidean geometry that has the property that a line has no parallels through a given point. Contrast this with Euclidean geometry, in which a line has one parallel through a given point. Higher-dimensional spherical geometries exist – elliptic geometry (be careful that it does does not imply any direct connection with the curve called an ellipse).
Ellipsoid shape is widely know due to the fact Earth is considered to be in this shape (approximately). An Earth ellipsoid is a mathematical figure approximating the shape of the Earth, used as a reference frame for computations in geodesy, astronomy and the geosciences. Various different ellipsoids have been used as approximations. Moreover, this shape is way more accurate to use compared to the sphere.
For those that don’t know what geodesy is – it is a branch of applied mathematics and earth sciences. It is the scientific discipline that deals with the measurement and representation of the Earth, including its gravitational field, in a three-dimensional time-varying space.
Hope you enjoyed this short intro into ellipsoids, spherical geometry and geodesy. Let me know if you would like to read more about these topics.
Don’t forget that maths is everywhere! Enjoy! ~LThMath