The Heart of Mathematics

At five litres per minute the average human heart pumps nearly 200 megalitres of blood through the body in a lifetime. Heart disease causes 40 percent of deaths in the EU and costs hundreds of billions of Euros every year. Mathematics can help to improve our knowledge of heart disease and our understanding of cardiac malfunction [TM131 or search for “thatsmaths” at].


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Moebiquity: Ubiquity and Versitility of the Möbius Band

The Möbius strip or Möbius band, with one side and one edge, has been a source of fascination since its discovery in 1858, independently by August Möbius and Johann Listing. It is easily formed from a strip of paper by giving it a half-twist before joining the ends.


Möbius band in 3-space and a flat representation in 2-space.

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Energy Cascades in Van Gogh’s Starry Night

Big whirls have little whirls that feed on their velocity,
And little whirls have lesser whirls, and so on to viscosity.

We are all familiar with the measurement of speed, the distance travelled in a given time. Allowing for the direction as well as the magnitude of movement, we get velocity, a vector quantity. In the flow of a viscous fluid, such as treacle pouring off a spoon, the velocity is smooth and steady. Such flow is called laminar, and variations of velocity from place to place are small. By contrast, the motion of the atmosphere, a fluid with low viscosity, can be irregular and rapidly fluctuating. We experience this when out and about on a gusty day. Such chaotic fluid flow is called turbulence, and this topic continues to challenge the most brilliant scientists [TM130 or search for “thatsmaths” at].


Vincent Van Gogh’s Starry Night.

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Doughnuts and Tonnetze

The circle of fifths is a remarkably useful diagram for the analysis of music. It shows the twelve notes of the chromatic scale arranged in a circle, with notes that are harmonically related (like C and G) being close together and notes that are discordant (like C and C) more distant from each other.


The Tonnetz diagram (note that the arrangement here is inverted relative to that used in the text.  It appears that there is no rigid standard, and several arrangements are in use) [Image from WikimediaCommons].

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Darker Mornings, Brighter Evenings

Today is the winter solstice, the shortest day of the year. We might expect that the latest sunrise and earliest sunset also occur today. In fact, the earliest sunset, the darkest day of the year, was on 13 December, over a week ago, and the latest sunrise is still more than a week away. This curious behaviour is due to the unsteady path of the Earth around the Sun. Our clocks, which run regularly at what is called mean time, move in and out of synchronization with solar time [TM129 or search for “thatsmaths” at].


Sunrise in Newgrange on winter solstice [image from

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Vanishing Hyperballs


Spherical ball contained within a cubic region
[Image from ].

We all know that the area of a disk — the interior of a circle — is {\pi r^2} where {r} is the radius. Some of us may also remember that the volume of a ball — the interior of a sphere — is {\frac{4}{3}\pi r^3}.

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The Star of Bethlehem … or was it a Planet?

People of old were more aware than we are of the night sky and took a keen interest in unusual happenings above them. The configuration of the stars was believed to be linked to human affairs and many astronomical phenomena were interpreted as signs of good or evil in the offing. The Three Wise Men or Magi were astrologers, experts in celestial matters, and would have drawn inferences from what they observed in the sky [TM128 or search for “thatsmaths” at].

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