Tag Archives: maths

Awesome maths geekery

Pi pieI loved this story. Google bid random mathematical numbers for the Nortel patents, including Pi billion dollars. Fantastic. Trying to imagine Dr Evil demanding that in a blackmail demand, and I can’t quite do it – so it must be true that Google isn’t evil…

At the auction for Nortel Networks’ wireless patents this week, Google’s bids were mystifying, such as $1,902,160,540 and $2,614,972,128.

Math whizzes might recognize these numbers as Brun’s constant and Meissel-Mertens constant, but it puzzled many of the people involved in the auction, according to three people with direct knowledge of the situation on Friday.

Are rechargeable batteries worth the money?

DIY Light Tent

I should probably have done this before I bought the rechargeables, but here’s some quick maths working out the ROI on some rechargeable batteries – are they worth investing in for your house?

8 batteries and charger  cost £17 – thanks Duracell / Amazon.

1 pack of four regular batteries costs, let’s say, £1.50 and I’d use one per month (principally in a baby monitor!).

Let’s say I have to recharge twice as often as I’d replace the batteries – twice a month – and that they would last for two years, after which I’d have to spend another £9 on fresh batteries. So let’s work out the total cost of ownership over 2 years for a comparison.

How much does it cost to charge the batteries? Well, this site gives me the maths. I can’t find specific power usage for my charger  but let’s assume its the same and do the maths on that basis.

First, EON’s local electricity cost for my postcode is about 23.3p per kwh. Actually, it’s slightly less as I get direct debit and dual fuel discounts of around 8%, but let’s call it that.

Then – I apply the maths – 9 hour charge * 300ma * 12v = 32.4 watt hours (from the Protog website above)

32.4 / 1000 * 23p = 0.74p

x2 (as assume 50% efficiency) = 1.49p per charge

In two years, that would be 52 charges minimum = around 77p.

TCO in two years of the charger, batteries and charging – £17.77. And assuming the charger lasts longer… the next two years would cost approx £9.77. Of course, I’m not modelling for energy price increases (folly!).

Buying the 24x packs of 4 AA batteries I’d otherwise need? Around £30 at least, if I buy in bulk, and more if you go on the £1.50 per pack price. So it’s about 100% cheaper to buy rechargeables (not to mention environmental impact, other types of batteries and devices etc).

In summary – good household ROI!

I’m not sure about all my assumptions, though – is the assumption of rechargeable battery life fair? Is the assumption of 48 recharges reasonable before performance degradation kicks in? Is the assumption on charging costs accurate? Is the assumption of the power capacity right, such that they’ll last us a couple of weeks of typical usage?

Interesting exercise – much as I’d like it if all consumerism could be evaluated for returns, I can already hear my wife making her geek noise at me….

Predicting running injuries with maths

I wish I’d been smart enough to work this out before the ITBS kicked in. Of course, it probably falls into the ‘spurious correlation’ category of statistical analysis, but there’s some sensible logic behind it… specifically:

That’s reasonable, of course: as you train, your speed increases each time you run, however your body cumulates fatigue. Consequently, your performance will level off at a certain point in training, then your running times will once again increase. Panicked at losing speed, you will push yourself too hard and wind up injured.

It’s an interesting post. Not everyone will be up to the maths (I can’t be bothered, and its too late for me!), and common sense may work as well, but its interesting reading for runners. Via the ever-useful Lifehacker.