Posts Tagged 'Astronomy'

Quadrivium: The Noble Fourfold Way

According to Plato, a core of mathematical knowledge – later known as the Quadrivium – was essential for an understanding of the Universe. The curriculum was outlined in Plato’s Republic. The name Quadrivium means four ways, but this term was not used until the time of Boethius in the 6th century AD [see TM119 or search for “thatsmaths” at].


Image from here.

It is said that an inscription over the entrance to Plato’s Academy read “Let None But Geometers Enter Here”. This indicated that the Quadrivium was a prerequisite for the study of philosophy in ancient Greece.

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A New Window on the World

The motto of the Pythagoreans was “All is Number” and Pythagoras may have been the first person to imagine that the workings of the world might be understood in mathematical terms. This idea has now brought us to the point where, at a fundamental level, mathematics is the primary means of describing the physical world. Galileo put it this way: the book of nature is written in the language of mathematics [TM102, or search for “thatsmaths” at].


Visualization of gravitational waves. Image credit MPI/Gravitational Physics/ITP Frankfurt/ZI Berlin.

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Kepler’s Magnificent Mysterium Cosmographicum


Johannes Kepler’s amazing book, Mysterium Cosmographicum, was published in 1596. Kepler’s central idea was that the distance relationships between the six planets (only six were known at that time) could be represented by six spheres separated by the five Platonic solids. For each of these regular polyhedra, there is an inner and an outer sphere. The inner sphere is tangent to the centre of each face and the outer sphere contains all the vertices of the polyhedron.


Figure generated using Mathematica Demonstration [2].

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The Search is on for Planet Nine

Then felt I like some watcher of the skies
When a new planet swims into his ken.

John Keats: On First Looking into Chapman’s Homer

Pluto, discovered in 1930, orbits in the Kuiper Belt, a ring of asteroids and icy debris beyond Neptune. About ten years ago, it was reclassified as a “dwarf planet”, so now we have eight planets. Is there a ninth anywhere? A recent paper in the Astronomical Journal presents evidence of a large planet in an orbit far beyond Neptune. If confirmed, this would be a dramatic confirmation of our understanding of solar system dynamics [TM088, or search for “thatsmaths” at].


Orbits of six trans-Neptunian objects aligned in one direction, suggesting a perturbing body, Planet Nine (?). Caltech/Robert Hurt.

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Thomas Harriot: Mathematician, Astronomer and Navigator

Sir Walter Raleigh, adventurer, explorer and privateer, was among most colourful characters of Tudor times. He acquired extensive estates in Waterford and Cork, including Molana Abbey near Youghal, which he gave to his friend and advisor, the brilliant mathematician and astronomer Thomas Harriot.

Thomas Harriot (1560 - 1621)

Left: Sir Walter Raleigh (1552-1618). Right: Thomas Harriot (1560?-1621)

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The Great American Eclipse

Just two years from now, on Monday, August 21, 2017, the Moon’s shadow will sweep across the United States at a speed of over 2,000 km/hr. The Great American Eclipse of 2017 will generate a frenzy of activity. [TM074: search for “thatsmaths” at ].

Moon between NASA’s Solar Dynamics Observatory and the Sun, giving a partial solar eclipse from space on Jan. 30, 2014. Image NASA.

Moon between NASA’s Solar Dynamics Observatory and the Sun,
giving a partial solar eclipse from space on Jan. 30, 2014. Image NASA.

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Pluto’s Unruly Family

An astrodynamical miracle is happening in the sky above. Our ability to launch a space-probe from the revolving Earth to reach a moving target billions of kilometres away almost ten years later with pinpoint accuracy is truly astounding. “New Horizons” promises to enhance our knowledge of the solar system and it may help us to understand our own planet too.

Four tiny moons (on left) orbit the binary system of Pluto (top right) and Charon.

Four tiny moons (on left) orbit the binary system of Pluto (top centre right) and Charon [Image NASA]

[See this week’s That’s Maths column (TM071): search for “thatsmaths” at].

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