4 ms·
> 17. At any given moment on the earth's surface, there exist 2 antipodal points (on exactly opposite sides of the earth) with the same temperature and barometr
by nwallin 5y ago
> 17. At any given moment on the earth's surface, there exist 2 antipodal points (on exactly opposite sides of the earth) with the same temperature and barometric pressure: youtube.com/watch?v=cchIr1OXc8E
This is not necessarily true. They say a picture is worth 1000 words: https://media.deseretdigital.com/file/5894488349 https://media.deseretdigital.com/file/5894488349
Regardomg Gabriel's Horn and Banach-Tarski, the paradox is described as a trumpet, or a ball, made out of molecules, atoms, electrons, protons, neutrons, quarks-- but the mathematical proof is... not that. It's pretty common that intuition about objects made out of a finite number of parts breaks down when describing a construct with infinitely many parts.
- raldi 5y agoI don't get what thought that picture is supposed to provoke.
- ruuda 5y agoBorsuk-Ulam applies to surfaces homeomorphic to a sphere, but the picture shows that the earth's surface is a sphere with at least one handle, a donut with at least one hole.
- Kwantuum 5y agoThe earth has "holes" and as such the proof of that statement for a sphere does not apply to the earth.
- lasc4r 5y agoThank you, something about this didn't make total sense to me.