SiS Quickie: Aged to Perfection

A “perfect” number is one whose factors (other than itself) add up itself. (Remember that the factors of a number are the numbers that it is divisible by.) Six is perfect: its factors are one, two, and three, which add up to six.

The next perfect number after six is 28.

Numbers can be perfect. People can’t be, but some definitely come closer than others.

So I’d like to wish a happy 28th birthday to the SigFig.

Pi Day: Proof that math nerds are fun!

Happy Pi Day, folks! I’m departing from the usual pi day talk of circles and desserts to discuss fun with algebra, just like I promised in yesterday’s blogiversary post.

You’ve probably seen this kind of “jedi mind trick” in a forwarded e-mail or a shared Facebook post:

Think of a number. Add 3. Multiply by 2. Square it. Subtract 36. Divide by 4. Divide by your original number. Subtract your original number.

Your answer is 6.

It’s nifty, but it’s more of a jedi math trick than a jedi mind trick.

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Happy Birthday, SiS!

A year ago today I made the first two posts to Science in Suburbia. I know that, due to work/distractions, I haven’t posted consistently for the entire year, but it’s still my first blogiversary and I’m happy that I’ve turned up the posting frequency over the last couple of months.

Something else I’ve seen with increasing frequency over the last couple of months? “Jokes” about how taking algebra was stupid and useless because you never use any of it after high school.

Besides an annoyed grumble, my reaction to this type of statement is twofold:

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SiS Quickie: In space, no one can hear you scream…

…and in an empty house, no one can hear you sing.

Since I work from home, I have the house to myself a lot. Between living with my folks, in a dorm, with roommates/upstairs and downstairs neighbors, and then with my folks again for a little while, this is really the first time in my life that this has been the case. What do I do with my newfound solitude?

I sing. Loudly and frequently.

I love singing and I HATE silence, which means I would hate being in outer space, where it’s impossible for sound waves to travel. (There’s also the part where I wouldn’t be able to breathe and my head would explode.)

Sound waves are mechanical waves. When a mechanical wave travels, particles have to move: the molecules in a rope move when you wave it back and forth, the water molecules in a pond move when you drop a stone and send ripples through it, and the molecules in air move when you make sounds. No medium to travel through = no molecules to move = no mechanical wave.

There are no such restrictions on light and heat, which are electromagnetic waves. Electromagnetic waves consist of moving electric and magnetic fields- no molecules required, no medium required. (Remember the ether that doesn’t actually exist?)

Light and heat from the sun can reach us through the vacuum of space because they are electromagnetic waves. Any scifi movie that depicts loud battles in space is scientifically inaccurate; there’s no medium for the sound waves to travel through. (Though if you expect scientific accuracy from your scifi movies, I pity you.)

Physics teacher protip: There is some variant of “Could we hear the moon explode? Explain.” on EVERY SINGLE introductory waves test. Be prepared.

SiS Quickie: Repeatability is Delicious…

…and soggy French toast is not.

Like fried rice, French toast is a dish that the SigFig and I both enjoy. We had a lot of eggs that we needed to use up, so I told him I’d make a batch. He asked me if I knew how. I made French toast once or twice back in college.

So of course I said yes.

The result was an unmitigated disaster.

The lesson to be learned here is that good food, like good science, must be repeatable. You can’t run an experiment once, get the results you want, and say that you’re done. You also can’t run an experiment several times, get drastically different results every time, and cherry-pick which data you draw your conclusions from. A scientific experiment has to be run several times, producing consistent results, in order for those results to be valid. The fact that I’ve made successful French toast once or twice does not, in fact, mean that I “know” how to make it. I’ll have to try again a few times- and succeed in all of those attempts- before I can reasonably make that claim.

All that being said, I’d still like to think that the results had less to do with my (lack of) culinary ability and more to do with the fact that the bread wasn’t thick enough.

Cosplay Geometry

Emerald City Comic Con (ECCC) is this weekend, and, while I can’t attend myself (I work weekends and I always wait till GeekGirlCon to request time off), I’ve been helping a friend with her Lady Sif costume. With no pattern to work from, our primary job was to look at photos and make posterboard templates of Lady Sif’s armor, which were then traced onto thin foam, cut out, and covered in metallic fabric.

She’s an artist and I’m definitely not. But my experience as a math tutor means I can draw polygons decently, so I started with the six quadrilateral abdominal plates. When we laid the first few templates that I made against the base of the costume, we found that I had the shape right. However, the size was definitely off. I needed to make the templates smaller, but I didn’t want to change the overall shape- I wanted my new shape to be similar to my old one. When two polygons are similar, all of the angles in one shape are the same as the angles in the other shape, and the length of each side has been multiplied (or divided) by the same factor.

similarquadrilaterals
These two quadrilaterals are similar. The curved lines indicate the angles that are congruent (equal to each other). The length of each side has been divided by 2.

I trimmed the appropriate amount off of each side. While the result looked good against the base of the costume, my friend noted that the new template was a lot smaller than the old one. Intuitively, we think that whatever happens to the side lengths of a polygon should be the same thing that happens to the area of the polygon- if each side length is cut in half, the area should be cut in half, right?

Not exactly.

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