## Monday, August 15, 2011

### Crosswalks: It's measurably more 'green' to wait for a break in traffic

0 comments Posted by burton mackenzie at 3:41 PM

Many people try to be *greener *by walking instead of riding in a bus or car, and that's great. For pedestrians, crosswalks are a good demand-based way to stop traffic and get safely across the road. However, if you don't use crosswalks *judiciously*, you're not being as green as you think.

^{2}= 0.5 * 2702 kg * (14 m/s)^2 = 260 kJ for the average vehicle, or between 2.6MJ and 7.9 MJ for 10-30 average vehicles.

**it costs the environment 370 ml to 1.1 litres of burnt gasoline every time I stop traffic to cross the road!**

**0.85 kg to 2.5 kg of CO2 dumped into the atmosphere**so I can cross the street.

__Problem Workaround__: Pedestrians have a reasonable need to cross the street. The greenest way to do this at a crosswalk is to

**wait for a break in traffic**so the least amount of cars have to stop.

**Reduce**is the biggest, most important aspect of "Reduce, Reuse, Recycle".

## Saturday, February 12, 2011

I've had people write a lot of things about what I've written, but my current favourite is **"*** You are the sort of lunatic that should be running the country*". Thanks D.Quinn!

Labels: bi-yearly post

## Monday, August 03, 2009

## Friday, May 01, 2009

I am not a lawyer. Seek __local__ legal counsel first; you are responsible for your actions, not me.

## Friday, April 24, 2009

Did you know that (42^{2} + 111^{2})(2^{2} + 5^{2}) = (471^{2} + 432^{2}) = (639^{2} + 12^{2})?

^{2}+ b

^{2})*(c

^{2}+ d

^{2})

which factors to the complex roots

rearrange the factors to get

which multiplies out to

but since this is a complex conjugate, it simplifies to

^{2}+ (ad + bc)

^{2}

That is, given any product of sum of squares, you can easily find what other sum of squares represents the answer.

Further, we can also re-order the factors to give

^{2}+ (bc - ad)

^{2}

Which is yet another solution represented as a sum of squares!

Try it! (42

^{2}+ 111

^{2})(2

^{2}+ 5

^{2}) = (471

^{2}+ 432

^{2}) = (639

^{2}+ 12

^{2})

Burton MacKenZie www.burtonmackenzie.com

## Saturday, March 14, 2009

## Sunday, February 22, 2009

Burton MacKenZie www.burtonmackenzie.com

p.s. Here is an earlier post about Mercury.

## Sunday, February 01, 2009

### Why do so many people wonder if Ann Coulter is a man?

0 comments Posted by burton mackenzie at 1:11 PMLast year I was playing with the automated Gender Guesser. There were stirrings on the net that Ann Coulter, an american who makes a living by spewing controversial nonsense and hatred to the ignorant masses, was really a man. I went to her website and input some of her posts into the Gender Guesser.

__most popular post__on my entire blog, a popularity almost exclusively based on daily google searches for "Ann Coulter is a Man" or "Is Ann Coulter a Man?". I am not proud of this - my blog is mostly math and science based. It is a thorn in my side that my most popular post is due to people searching for information on her true gender and that, on average, it far outcompetes my regular posts. I considered removing the original post entirely, but that didn't seem right, either. I was reluctant to even add this post, but in the end decided to publish the bizarre website traffic happenings that I've been seeing for months. This has been going on for a while but I didn't want to lead in January by mentioning it. Mentioning Ann is a bad Juju way to start a year.

__every__

__freakin__

__day__come to my blog from google searches wondering if you're a man. WTF? No, seriously.

## Friday, January 30, 2009

### Peasant Finger Multiplication Proof for all Bilaterally Symmetric Species

3 comments Posted by burton mackenzie at 2:24 AMThere is a technique for multiplying numbers between 6 and 10 on your fingers called peasant multiplication (graphic illustration). I explained how to do it two years ago, and I mentioned an easy proof of it. Since I was subsequently asked for the proof, I present it now with an improvement. (If you don't already know how to perform the multiplication, please check the links above, first)

__Why Peasant Finger Multiplication works for any Bilaterally Symmetric Species__

^{2}

__tens digit__(base 10) is represented by adding the number of fingers on each hand representing digits. Here I multiply it by 10 to represent that it will be placed in the 10s digit:

_{10}= 10*(a + b)

_{d}= 2*d*(a + b)

_{ones}= (d - a)*(d - b)

_{ones}= d

^{2}- d*(a + b) + ab

_{d}+ p

_{ones}= 2*d*(a + b) + d

^{2}- d*(a + b) + ab

^{2 = }(a + d)*(b + d)

## Saturday, January 24, 2009

I came across a technique for multiplying big numbers recently, called prosthaphaeresis [1], that predates the use of logarithms. It relied on the use of pre-calculated cosine tables, and made use of the trigonometric relation: