For many decades, a search has been under way to find a theory of everything, that accounts for all the fundamental physical forces, including gravity. The dictum “physics is geometry” is a guiding principle of modern theoretical physics. Einstein’s General Theory of Relativity, which emerged just one hundred years ago, is a crowning example of this synergy. He showed how matter distorts the geometry of space and this geometry determines the motion of matter. The central idea is encapsulated in an epigram of John A Wheeler:
Posts Tagged 'Geometry'
Symplectic Geometry
Published May 30, 2019 Occasional Leave a CommentTags: Geometry, Hamilton, Physics
From cheetahs chasing gazelles, through coastguards saving shipwrecked sailors, to missiles launched at enemy aircraft, strategies of pursuit and evasion play a role in many areas of life (and death). From pre-historic times we have been solving such pursuit problems. The survival of our early ancestors depended on their ability to acquire food. This involved chasing and killing animals, and success depended on an understanding of relative speeds and optimal pursuit paths.
Gaussian Curvature: the Theorema Egregium
Published December 27, 2018 Occasional Leave a CommentTags: Gauss, Geometry
Surfaces of positive curvature (top), negative curvature (middle) and vanishing curvature (bottom) [image credit: NASA].
characterizes the intrinsic geometry of a surface.
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A Trapezoidal Prism on the Serpentine
Published September 13, 2018 Occasional Leave a CommentTags: Geometry
Walking in Hyde Park recently, I spied what appeared to be a huge red pyramid in the middle of the Serpentine. On closer approach, and with a changing angle of view, it became clear that it was prismatic in shape, composed of numerous barrels in red, blue and purple.
Changing perspective on approach to the Mastaba
The Miraculous Spiral on Booterstown Strand
Published August 16, 2018 Irish Times Leave a CommentTags: biology, Geometry, Geophysics
We all know what a spiral looks like. Or do we? Ask your friends to describe one and they will probably trace out the form of a winding staircase. But that is actually a helix, a curve in three-dimensional space. A spiral is confined to a plane – it is a flat curve. In general terms, a spiral is formed by a point moving around a fixed centre while its distance increases or decreases as it revolves [see TM145, or search for “thatsmaths” at irishtimes.com].
The spiral sandbank on Booterstown strand (satellite image digitally enhanced by Andrew Lynch).
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Optical Refinements at the Parthenon
Published June 21, 2018 Irish Times Leave a CommentTags: Geometry, History
The Parthenon is a masterpiece of symmetry and proportion. This temple to the Goddess Athena was built with pure white marble quarried at Pentelikon, about 20km from Athens. It was erected without mortar or cement, the stones being carved to great accuracy and locked together by iron clamps. The building and sculptures were completed in just 15 years, between 447 and 432 BC. [TM141 or search for “thatsmaths” at irishtimes.com].
A Glowing Geometric Proof that Root-2 is Irrational
Published May 24, 2018 Occasional 1 CommentTags: Geometry
It was a great shock to the Pythagoreans to discover that the diagonal of a unit square could not be expressed as a ratio of whole numbers. This discovery represented a fundamental fracture between the mathematical domains of Arithmetic and Geometry: since the Greeks recognized only whole numbers and ratios of whole numbers, the result meant that there was no number to describe the diagonal of a unit square.
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