Sunday, 29 August 2010
Gizmodo has an interesting article about how the iPhone (and probably other digital cameras) can distort fast-moving objects, with propellers being the most common example. This iPhone video of a propeller is from the comments; there are lots of other examples in the article. Weird effects happen because "as it turns out, most digital cameras don't actually take a picture the instant you hit the button. What they actually do to capture an image is scan over the frame either vertically or horizontally. So basically, not all parts of an image are recorded at exactly same time (the top right could be a little ahead of the bottom left, etc.). Hence it being called rolling shutter."
It is cool to think that if our eyes had rolling shutters, this is how we might see the world too, with fast moving objects seeming to move in and out of existence or bend in strange ways. It's a great example of how perception is not necessarily reality.
Wednesday, 25 August 2010
The meaning of Play Station controller symbols.
Image via Wikipedia
This is interesting: Gizmodo has an article on the meaning of the symbols on a PlayStation controller. Teiyu Goto, an engineer involved in designing them, claims that "Other game companies at the time assigned alphabet letters or colors to the buttons. We wanted something simple to remember, which is why we went with icons or symbols, and I came up with the triangle-circle-X-square combination immediately afterward. I gave each symbol a meaning and a color. The triangle refers to viewpoint; I had it represent one's head or direction and made it green. Square refers to a piece of paper; I had it represent menus or documents and made it pink. The circle and X represent 'yes' or 'no' decision-making and I made them red and blue respectively. People thought those colors were mixed up, and I had to reinforce to management that that's what I wanted."
This is interesting: Gizmodo has an article on the meaning of the symbols on a PlayStation controller. Teiyu Goto, an engineer involved in designing them, claims that "Other game companies at the time assigned alphabet letters or colors to the buttons. We wanted something simple to remember, which is why we went with icons or symbols, and I came up with the triangle-circle-X-square combination immediately afterward. I gave each symbol a meaning and a color. The triangle refers to viewpoint; I had it represent one's head or direction and made it green. Square refers to a piece of paper; I had it represent menus or documents and made it pink. The circle and X represent 'yes' or 'no' decision-making and I made them red and blue respectively. People thought those colors were mixed up, and I had to reinforce to management that that's what I wanted."
Thursday, 19 August 2010
Star Wars Uncut
Star Wars Uncut "The Escape" from Casey Pugh on Vimeo.
I am hugely impressed by this attempt to re-shoot the entire Star Wars canon by cutting up the films into 15 second pieces and letting fans re-make those 15 seconds however they like. A truly great idea. A small sample is shown above.
Via BoingBoing.net
Thursday, 12 August 2010
Monday, 9 August 2010
Even-length palindromic numbers mod 11 = 0
I was surprised to learn from a comment on Project Euler that palindromic numbers are always divisible by 11.
Here's the proof (for six digit numbers):
i.) A palindromic number has the form abccba [By definition]
ii.) abccba = 100000a + 10000b + 1000c + 100c + 10b + a [Expansion in Base 10]
iii.) abccba = (100000a + a) + (10000b + 10b) + (1000c + 100c) [Re-organizing ii.)]
iv.) abccba = 100001a + 10010b + 1100c [Re-organizing iii.)]
v.) abccba = 11 (9091a + 910b + 100c) [Factor out 11 from iv.)]
QED [= Proved, since we have factored 11 out.]
I think this always holds for palindromes (of any length) with an even number of characters, but it does not necessarily hold if you are allowed to include an 'odd' digit in the centre. (I know it sometimes holds because 121 = 11 x 11, but I don't know if 121 is a special case.)
Here's the proof (for six digit numbers):
i.) A palindromic number has the form abccba [By definition]
ii.) abccba = 100000a + 10000b + 1000c + 100c + 10b + a [Expansion in Base 10]
iii.) abccba = (100000a + a) + (10000b + 10b) + (1000c + 100c) [Re-organizing ii.)]
iv.) abccba = 100001a + 10010b + 1100c [Re-organizing iii.)]
v.) abccba = 11 (9091a + 910b + 100c) [Factor out 11 from iv.)]
QED [= Proved, since we have factored 11 out.]
I think this always holds for palindromes (of any length) with an even number of characters, but it does not necessarily hold if you are allowed to include an 'odd' digit in the centre. (I know it sometimes holds because 121 = 11 x 11, but I don't know if 121 is a special case.)
Labels:
Factoring,
Math,
Number Theory,
Project Euler,
Recreation,
Specific Numbers
Thursday, 5 August 2010
M of the M
This is a photo taken out of a larger album (composed of 505 photos to be exact) solely of Mario and Luigi around North America. This album is found here. Photo credit given to revengingangel. Mario of the Month for August 2010
Wednesday, 4 August 2010
Tuesday, 3 August 2010
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