Geometry was always one of my favourite subjects in school, and the love affair continued with parabolas, hyperbolas, ellipsoids and such awesome stuff in the higher standards. But then, we parted ways, for more than a decade.
So, when Manuja taai showed me the book मला उत्तर हवंय - लेखक मोहन आपटे, I could barely wait to go home and start drawing these. Here are my initial attempts to draw some simple figures: an Astroid, a Moire pattern, a Sierpinsky fractal triangle and a parabola. More will come. You have been warned!
One area of geometry that we barely touched during our graduate course, and which I would have loved to learn more about, was topology, which is the study of surfaces and their transformations by bending, pressing or twisting. For example, consider 2D alphabets O and D- you can easily convert them into each other. Same goes for (A and R), (H and K),and (E, T and Y). But letters B and X are not topologically similar.
This gets even more exciting when you go to 3D. A coffee mug and a donut may look totally different, but they are topologically similar.
We 3D creatures cast a 2 dimensional shadow. So if there's a 4D being out there, their shadow would be... 3D!
When a sphere (3D) passes through a paper (2D), the 2D folks would see that as a CIRCLE that grows bigger and then smaller. If a hypercube (4D cube) passed through our world (3D), we would see it as a cube that suddenly appeared, grew bigger, and then smaller before it vanished.
Hypercubes, hyperspheres and hyperspaces... The 4D world is hyper-fascinating indeed!
If there exists a 4-dimensional being out there, it would be able to see inside us, as easily as we see inside a 2-dimensional figure like a circle, square or a triangle.
Obvious as a mathematical fact, but not so intuitive a a 'practical' reality.
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