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Tuesday, June 13, 2006

The other day while I was out strolling, my family and I came upon a broken and discarded projection tv. I was pointing out the various parts of it and what they do when I realized "Hey, these three projection lenses are 2.5/3 intact!".

I wrote down the address of the place and came back later with tools. I had no idea what to do with them at the time, but figured 5-1/4" lenses would lend themselves to something. They seem to project well when a strongly lit (from behind) image is placed flat on the rear lense.

I looked up the lens on the net, and the first link was to an astronomical satellite proposal (powerpoint format) describing an orbiting composite x-ray telescope(s) that would be able to directly image black holes ("The Field of View of a Thin Lens Interferometer"). It's coincidental, but not related to the reported research I mentioned in I want Black Holes for Christmas! a couple of weeks back.

The X-ray satellite project made me think "Hey! They could concentrate light for my digital camera!". I tried it. I liked it.

There are some artefacts in the image (blue near centre, reflections, spectral abberation on the right side), but I didn't spend much time eliminating problems. This particular image was taken by hand-distancing the camera lense from the projection tv lense (i.e. poor focus stability). It sure grabbed more light. I think next I must make a jig to hold a camera at the right distance to the lense and take some starfield photos with my new five-incher!

Sexy photos to follow.

Burton MacKenZie

Sunday, June 11, 2006

After I mentioned how to square a number near fifty (50) in your head, a friend of mine taught me how to square numbers ending in five (5) in your head.

The numbers meant by "ending in five" are 15, 25, 35, 45, etc. (5 itself is a degenerate case that need not be included) These numbers can be represented as x = 10*a + 5, where a=1, 2, 3, 4, etc for the series listed above. To get the square, x^2 = (10*a + 5)^2 = 100 * a * (a+1) + 25. All you have to remember is that the square of one of these numbers has 25 as the lower two digits, followed by the original tens digit multiplied by the original tens digit plus one.

For example, 75^2 = [(7 * 8)][25] = [56][25] = 5625. (where [] represents literal digits)

In practice, your only limit for how high you can go is how big a value of 'a' you can multiply in your head with 'a+1'. (or alternately, a^2 + a, as below)

This can also be combined with other math tricks, like the aforementioned squares near fifty in your head to do much bigger number crunching in your noggin.

For example, 535^2 = [(53 * 54)][25] = [(53*53 + 53)][25] = [((2500 + 300 + 9) + 53)][25] = [(2809 + 53)][25] = [2862][25] = 286225

Whee! I'm learning to square three digit numbers in my head!

Burton MacKenZie

Note: I changed an example above (for clarity) from 45^2 to 75^2.

People have been debating the lower limit of a planet for a long time. I just spent a whopping 30 seconds thinking of a good definition for the lower limit of what can define a planet. I think "planet" should be defined as "any celestial body that orbits a star, off of which a typical human could not jump themselves into orbit". If you can jump into orbit, it's not a planet. If you can't, it is. I define an orbit as moving 2*pi or greater rotations (in radians) around another mass to which you are gravitationally bound without touching the ground. Comments?

Burton MacKenZie

Sunday, June 04, 2006

A Sky without Scattering

The blue end of the visible spectrum is scattered in our atmosphere, which gives the sky its blue colour. The other day I thought "What would the daytime sky look like if our atmosphere didn't scatter light?"

This photo is a fair representation of how our sunlit sky would look like if our atmosphere didn't scatter light.

The sky would be black, except for the lightsources - stars (especially including our own), galaxies, planets, the moon, and the occasional asteroid, meteor or comet. In the picture above, the Sun shines brightly during the day, a star is visible nearby,
and the clouds are illuminated by the sun (I allow them scatter for this shot).

Everything on the surface Earth would either be in full sunlight (or moonlight or both), umbra, or shadow (no light). The colours of everything around us would still be as it is now, well lit and subtly varying in colour, but the "hard dark" areas where no light falls in shadow may seem to us now as darkly disturbing as the waving shadows of a tree in a bad dream or a grainy old black and white horror movie. Would cloudy days dazzle our dark-sky-adapted eyes? It would be a sky like we see in lunar landing photos, except with clouds.


Burton MacKenZie


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