Archive for February 9th, 2010

Pi π

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\pi is a mathematical ratio. It is the ratio between the circumference (length around) of a circle, and it’s diameter. No matter what circumference or diameter a circle has, the ratio will always be Pi. Pi is an irrational number. It never repeats i.e. it has no apparent pattern. It is indefinite, meaning it can never end. Even today some of it’s numbers are not known. As an analogy to see how big and indefinte Pi is, think, that if all the ink in the universe was put together, it still wouldn’t be enough to write down Pi in numerical form.

\pi is the sixteenth letter of the Greek alphabet, and it literally means ‘p’ (the letter p). Pi has been known since the early egyptians. They did not know everything about Pi, but they knew it was a little more than 3. Archimedes was the first mathematician to really rigorously study Pi. He came up with an approximate value of 3.14185. All through the ages, different versions of Pi appeared but none contained more than ten digits. After the 2nd Millenium AD, Pi got changed and as much as over 200 new digits were found. During the 20th century, Pi calculations became even more precise with the help from computers. In 1949, John von Neumann used ENIAC (Electronic Numerical Intergrator And Computer) to compute 2037 digits, a calculation which lasted 70hrs.

Did you know: The current Guinness World Record of the most digits of Pi remembered belongs to Lu Chao, from China. He recited 67,890 digits in 24hrs and 4 minutes. The rules were no breaks or pauses and with no little more than 15 seconds in between each digit, and no mistakes. In an interview, he claimed he knew 90,000, but he made a mistake on the 67,891st digit, stopping short his record.

Here is a very nice video I found on youtube concerning Pi:

References: [...][...]

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Consuming Electricity (Experiment)

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As a sort of experiment, I decided to see how much certain appliances in my house cost my parents. At first, as a control, I unplugged everything and I even switched off the fridge. This is to prevent another thing consuming electricity and compromising the results. On my list of appliances was: 1) the electric kettle, 2) the toaster, 3) all the integrated lights turned on, 4) the projector, sound system, and blu-ray player, (everything needed to watch a movie). I tried each one individually, switching them off as I was finished with them to make sure the next appliance was the only thing consuming. The way I got my results was that I timed myself for one minute and counted how many times I saw the red line (black in my case) on the rotating piece of metal under the numbers indicating the watts consumed. I tried each appliance three times to make sure I got an average and here is what the results looked like:

Here is an average of the rotations:

On the electric meter, it was indicated that 187.5 revolutions (rotations of the line) was equal to 1 kilo watt. This means that if the line revolved 187 and a half times, the numbers on top would be bigger by one unit. To find out how many watts were used in only one turn, I did a simple 3 rule. 1000 watts is equal to 1 kilo watt.

\frac{1000w}{187.5}=5.3w per turn

And then, I calculated how much each appliance used in watts by multiplying the number of watts per rotation with the number of turns I counted for the appliances..

Kettle= 9*5.3=47.7w

Toaster= 5*5.3=41.5w

Lights= 2*5.3=10.6w

Projector and Co.= 2*5.3=10.6w

I then went on to find out how much it cost money-wise. On a recent electricity bill, I saw the price at:

14.10 cents per kilo watt.

The problem was that my previous calculations weren’t in kilo watts but in watts. Once I had the watts, I had to simply divide by 1000 to convert them to kilo watts, and multiply by the price (14.10 cents) and then convert the price to euros (divide by 100).
Here is a table with the appliance, the number of watts consumed, and the price:

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