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π approximation: Machin’s formula

In the excellent $\pi$ approximation video, Katie Steckles asked for $\pi$ approximations. I teach a first year techniques module (mostly calculus and a little complex numbers and linear algebra). This year I have changed a few bits in my module; in particular I gave some of my more numerical topics to the numerical methods module and took in return some of the more analytic bits from that module. This gives both modules greater coherence, but it means I have lost one of my favourite examples, from the Taylor series topic, which uses a Maclaurin series to approximate $\pi$.

Ivor Grattan-Guinness 1941-2014

An obituary has been published in The Guardian for Ivor Grattan-Guinness, historian of mathematics and logic, who died of heart failure on 12th December 2014. This begins by explaining that when Ivor became interested in the history of mathematics in the 1960s,

it was an area of study widely considered to be irrelevant to mathematics proper, or something that older mathematicians did on retirement. As an undergraduate at Oxford, he found that mathematics was presented drily, with no inkling of the original motivations behind its development. So Ivor set himself the task of asking “What happened in the past?” — as opposed, he said, to taking the heritage viewpoint of asking “How did we get here?”

Read more: Ivor Grattan-Guinness obituary (The Guardian).

Via Dave Richeson on Twitter.

More to be done between universities and industry

I saw the video below, which is Rachel Riley being asked questions about her maths education at a Your Life event, in a tweet by Rob Loe, who quoted a section of one answer around 4:50 where Rachel says: “stop saying proudly that ‘I’m really bad at maths’ because you wouldn’t say ‘I can’t read’, you wouldn’t say ‘I can’t write’ as a proud thing.”

What particularly caught my ear was this section (around 5:30):

L’Aquila earthquake convictions overturned

You may remember a couple of years ago there was a conviction of seven men in Italy, widely reported as being for failing to predict an earthquake. Actually, there was a little more to it — the conviction related to a supposed “falsely reassuring statement” given to the public — but, still, the scientific community’s outrage centred around the impossibility of accurately predicting earthquakes based on earlier tremors.

It was reported this week that the manslaughter conviction for six of the men has been overturned in an appeals court, with the seventh — then deputy head of Italy’s Civil Protection Department Bernardo De Bernardinis, who made public statements that the tremors posed “no danger” — having his sentence reduced from six to two years. Physics World says it is likely that these verdicts will be challenged in Italy’s Supreme Court, which may not hear the case until 2016.

More information

Physics World: L’Aquila verdict quashed.

Background (2012)

Aperiodical: L’Aquila seismologists found guilty of manslaughter connected to earthquake risk assessment.

Math/Maths 119: Those Boffins, and their Science.