eon

Posted by tpc at September 28th, 2008

Any rigid body displacement where a point is fixed is equivalent to a rotation. I saw this neat proof from Don Koks’ Explorations in Mathematical Physics.

By the hypothesis

Hence is orthogonal and But should vary continuously from the identity transformation, allowing us to conclude So


since we are working in 3D. We are forced to conclude
for some .
Thus has an eigenvector with eigenvalue 1. The transformation is thus the rotation about the direction .

Posted by tpc at September 24th, 2008

While perusing some blogs, while waiting for the rain to stop, I’ve found more evidence to support learning maths than replying on calculators.

A TRAFFIC warden gave parking fines to innocent motorists – because he did not know how to tell the time.

The bungling parking attendant had to use a calculator to work out the expiry time on tickets displayed in motorists’ windscreens.

But with calculators working in decimals rather than minutes and hours, the ticket-happy warden had his book out before realising his maths was letting him down.

One of his victims was IT manager Dave Alsop, who tried his best to show the warden the errors of his arithmetic ways. But to no avail.

The 29-year-old from Torbay had parked in the Terrace car park close to Torquay harbour and paid £1.20p for 75 minutes. His ticket was issued at 2.49pm and would have covered him until 4.04pm.

But when he returned at 3.41pm, he discovered he had been given a £50 parking fine.

He found the traffic warden nearby and asked him why he had been booked when his ticket clearly showed he had time remaining.

The warden disagreed and tried to prove his point using a calculator.

He tapped in 14.49 and added 0.75 to produce a total of 15.24, which he claimed meant Mr Alsop’s ticket expired at 3.24pm – 17 minutes before he returned to his car.

Mr Alsop said: “I tried to explain to the warden but he didn’t have a clue. He thought he was doing things correctly. He just carried on doing other cars parked there.”

The warden insisted he was right and issued fines to two other unsuspecting motorists.

Mr Alsop, who works for Pavey Insurance brokers in Torquay’s Abbey Road, appealed, had his fine waived and received an apology from Torbay Council.

Via -> Natural Blogarithms -> 360 -> God Plays Dice -> Eric Berlin

Posted by tpc at September 23rd, 2008

Yes, it is plural because two such primes were found within two weeks. See the
press release from GIMPS. I guess we can’t really comprehend how big a 10 million digit number is. My ruler tells me that the normal font size of this blog gives 6 characters per cm, hence 600 characters or digits per metre. 10 million / 600, gives about 16.6 km. That’s how long the number would be written out in a line. It would take me almost 2 hours to run 17km. But that’s just writing it out! We haven’t even talked about doing arithmetic on it, let alone checking that it is indeed a prime number!

UCLA who found the larger of the two primes first is getting about $50,000 of the prize money. There goes my dream of making an impact in mathematics and getting some useful cash out of it. And no, I’m realistic enough to not dream about solving Riemann’s hypothesis or the BSD. In my younger days, I dreamt about Goldbach’s conjecture, which is still open but without cash prizes. Even that may be knocked down within the next few years. We do live in exciting times.

Still it is momentous to break the 10 million mark, important enough for me to brush the dust off this blog and write something. Join GIMPS and keep searching. 100 million is not very far away.