Conic sections in the sand give shipwrecked Socratic philosopher, Aristippus, good hope.
I wonder if this ancient tale, in which the mathematics of planetary motion some 2000 years prior to it’s application in space travel, is used to signify the presence of intelligent life and therefore hope of salvation has some echo in our modern era.
What obscure and impenetrable modern theorems could be left on a 21st century beach to do the same job?
In the geometry of mariners, where straight lines are Great Circles, the angle sum of a triangle is more than 180 degrees.
The sine function starts life in a triangle (year 9?) then becomes intimate with a circle at A level, as y-coord of a point rotating on a unit circle. Later it is about infinite series or, even, differential equations.
Edexcel’s January 2013 Mechanics 2 exam paper has massively intricate last part of last question to determine existence of third collision. Examiner’s report says not many candidates supplied an answer, which is not a surprise. This, and much more, is freely available on my exam bucket website: http://jped.co.uk/ExamBucket/exambucket.php.