Some things don’t change. This Theorem of Euclid’s, now IGCSE geometry, has probably been taught at The King’s School Canterbury since foundation in 597 AD (not always as an animated gif though).
Infinitely small triangles provide clue to finding the slope of curves.
Area sandwich proves that finding areas is opposite to differentiation – The Fundamental Theorem of Calculus
Mathematics, science or art?
24 Jan 15
Geophysical Computational Fluid Dynamics computes the wind field across the Earth. Earthnullschool streams this, here at 30,000ft, on it’s intriguing and beautiful virtual globe. A quasi-stationary solution pattern for wind equations results for present over the Atlantic Ocean – ‘Rex Block’ – caused by interaction of ocean, mountains and wave dynamics. It all results in bifurcation of jet stream into Sub Tropical Jet, over Africa and Polar Jet round Iceland and UK.
Up and Down – distance time graph. Hand level is zero displacement, ball goes up, passes through hand level and finish with negative displacement on ground.
The Natural Logarithm is an integration defined function. The shaded area under the graph is the value of the natural logarithm of the upper limit in the integration.
Gauss Error Function.
There is no elementary function for the integral but the area function is crucial to mathematics and statistics.
The area under a graph turns out to follow the same addition rules as logarithms …
Mathematics, Science and the Beauty of the Earth.
13 January 2015. Modis satellite imagery (Dundee) shows down wind turbulence patterns from island of Madeira. Earthnullschool wind field shows the wind pattern that caused it together with the majestic Azores anticyclone and intense Trade Wind field to the south. Third slide is iPAD generated ‘Wind Tunnel’ (computational fluid dynamics) which can start to replicate the kind of patterns apparent on the imagery.
Some prime numbers calculated by a quadratic.