Parallel Lines of Longitude : what lines ? Aren't parallel lines supposed to never meet , but don't parallel longitudes actually meet - at our North and South Poles ?
What in the name of all public school math is going on here?
Forget public educational authorities bowing to political correctness pressure from those who deny human carbon pollution of the atmosphere and that species evolve over time.
Most of us believe the world is not flat but a sphere - a blue sphere - we've seen the photos of it taken out in space.
But the math we teach in school comes across like it was handed down on tablets of stone to Moses.
(Along with Commandant 11: "Thou shall not claim that fossil fuels will ever run out, though you also deny that fossils ever did run about.")
It is called Euclidean Geometry and it has the outstanding advantage of being simple to demonstrate on a classroom chalkboard and thus in making even ho-hum mathematicians seem god-like.
Where it isn't at all simple to demonstrate, is out in the physical world.
Out there it is not actually correct or true - at least not true like a law carved out on stone and handed down to you by G.O.D. Himself should be.
It is actually a 'quick and dirty', 'close enough for the P. Eng', type of rough and ready 'field math'.
Fail to believe, oh Earthling ?
Take your bog-ordinary orange -- it looks a lot like the Earth - which it should as both are spheres or balls.
Score it around the equator and then from North Pole to South Pole and back again - then turn it horizontally 180 degrees and again score it from Pole to Pole and back.
You now have divided the Earth-cum-orange's surface into 8 equal parts: triangles.
Or are they ?
A triangle, as your dimly remembered High School teacher was always quick to remind you, is such that all of its internal angles always add up to180 degrees.
Measure those 1/8ths of an orange carefully and then reflect.
Don't add up to 180 degrees do they ?
Welcome to the incredibly useful world of non-Elucidean math : the math of measuring land for land sales on this sphere we call Earth.
Well, actually, unless the piece of land is very big indeed we are unlikely to note the error in measurement if we don't use non-Elucidean geometry.
But it is there and it matters , or should matter, to the two thousand years of mathematicians who failed to even notice the error let alone chose to ignore it.
Yep, the would-be "Masters of the Universe" turned out to be "The Gang who Couldn't Measure Straight "!
Elucidean math is incredibly useful --- and long may we ordinary joes and josephines continue to use it in our ordinary daily lives.
But let us also hear from the world's collected mathematicians a big and sincere apology, a sort of scientific Truth and Reconciliation, over them foisting Euclid's Geometry upon us and upon themselves as the only,the only possible, presentation of physical reality.
Yeah - as if that is likely !
As if highly educated mathematicians are going to admit to us that they didn't notice the math implications of the fact that the world was round, long after even uneducated peasants knew it was round.
If stuff like this gets around, then where will their pensions and their prestige be ....