Winter Solstice 2013

In anticipation of the southern hemisphere winter solstice 2013 that will happen Friday this week, I thought I’d post a nice sun related graph.  This graph shows the average power generated by my rooftop photovoltaic solar panels over the course of two and a bit years. It’s interesting to see that despite some quite large week to week variations, the general trend is clearly in line with the seasons, with the peaks and troughs lining up with the summer and winter solstices.

Click on the image to get a larger view.



Probably Friday the 13th

Last Friday was a Friday the 13th. I read in the paper the other day that the 13th day of the month was more likely to fall on a Friday than any other month. I was a bit skeptical about this, but having checked it out, it is true, but only when you take into account that unusual leap year rule that says years divisible by 100 (but not 400) are not leap years.

This once in a 100 years aberration to the pattern of the calendar skews the distribution of weekdays such that over a 400 year period you get the 13th day of a month falling most often on a Friday (688 times), but least often on a Thursday (684 times.)

So the probabilities for the weekday of the 13th of the month comes out as follows …

Sunday: 14.3125%
Monday: 14.27083%
Tuesday: 14.27083%
Wednesday: 14.3125%
Thursday: 14.25%
Friday: 14.33333%
Saturday: 14.25%

[This content was originally posted to Google+]

The joy of algebra

I’ve been helping my 5th grade daughter with her Maths homework recently, and have been reminded of the joy of algebra. Quite a few of her homework questions involve complicated sentences about Joe being 3 times older than Jerry but 3 years later he’s only 2 times older. With 5th grade maths you can only guess at the answer with trial and error, but with algebra you just write down the equations and solve them with no guessing at all! How good is that? Sadly, my daughter is not yet convinced.

Update 20 Feb 2015: Sadly I went through the same struggle with my youngest son, trying to convince him of the benefits of algebra – even to the point of having the maths mantra – “There’s the hard way, or there’s algebra.”

[This content was originally posted to Google Buzz, #122]