mathmom's blog

Whenever I try to make dinner for some particular time, it ends up being served half an hour later. This is very frustrating. It is the more frustrating because as a mathematician, you would think I could figure this out. If f(t) is the time dinner is actually served at when the input is the time I am aiming for, then f(t)=t+30 minutes. So if I want the time I serve dinner at to be a particular time, I should just aim 30 minutes earlier: f(t-30)=t. But there is some subtle paradox I am having trouble with: the input has to be the time I'm trying to serve dinner at, so I can't plan for the output to be the time I'd like to have dinner. This analysis doesn't even include helpful children, making the calculation even trickier. Ah, the paradoxes of everyday life. It's a good thing I have my degree in math, or I'd never be able to analyze this... =)

Amanda has taken to doing math before bed instead of reading stories. I'm not sure I understand, but I do enjoy---we've looked at addition, subtraction, multiplication, roman numerals, symmetry, and so on. If you have any ideas for what to cover next, I'd love to hear them! One night I decided to look at math in music---specifically, some patterns in the violin piece she's been practicing. I told her that we would be doing music math that night, and she said skeptically, " Ooookaaaay ..." She seemed to enjoy the subject. But afterward, she said that she was a bit surprised. "I thought that by math music, you meant something like 'One violin plus one violin equals one banjo, and one banjo plus one banjo equals one guitar!" I guess I know what she thinks of banjos... =)

We were playing "guess the number" at breakfast today. It goes like this: "I'm thinking of a number between 1 and 10," "Is it 5?" "Higher." "7?" "Lower." "6?" "That's it!" Eleanor brought up the idea of using fractions, and her number turned out to be 3.5. Then Michael started in. "I'm thinking of a number between 3 and 4." 3 1/2? lower. 3 1/4? lower. 3 1/8? higher. I figured out as soon as he started that the number was pi, and so we had a discussion about the fact that you could get closer and closer with fractions, but never guess the exact right number. This is hard for much older kids, I'm not sure exactly what Eleanor got... Then we had to discuss what pi measures. The idea that you want to know the exact distance around a circle makes sense, although Eleanor figures that in the real world, you could just take a measurement and it would be good enough. I star...

....pation. The rule in our house during the school year is that the kids get dressed before they come downstairs. I explained to Luke that he had to get dressed, because today is his second day of school. He didn't seem outwardly excited, but as he was coming down the stairs he said, "I go in car!" Yes, after breakfast, I explained. He repeated himself a few times---why say something once when you can say it 10 times? I turned away to make breakfast and I heard the garage door unlock. Luke was trying to get into the car, but was stymied by the fact that the doors were closed. Michael had to talk Luke back into the house. I don't know what he said, but Luke did eventually come in and eat toast. Interestingly enough, I cut his toast into 4 triangles today. I'm not sure how much he had thought about triangles before, but he repeated the word (giangle!) and repeated counting the sides with me. I asked him how many triangles he had, and he counted them by him...

This is (apparently) the Pythagorean theorem sung in Swedish. http://www.youtube.com/watch?v=OuqF45MLYFQ It makes me wish I knew some Swedish. It seems to involve the proof, not just the theorem (which would make for a shorter song). I can't find out anything else about it. I can't quite read the letters on the diagram they're using, which might make more sense. And now back to your regularly scheduled kid stories.

I have figured out why I hate folding socks---it's a simple problem of mathematics. 7 days x 2 feet x 5 people = 70 socks---not counting all the times that Amanda loses her socks between outings and needs a new pair. The total number of possible pairs of socks is 70x69/2=2415. Given a random sock pick, the chance that you pick out the pair for that sock is 1 in 69. Once you've got that pair, the chance you pick out a pair on the next two grabs is 1/67... Assignment: what is the chance that, reaching randomly into the bin each time, you come up with exactly the right pairing of socks? If I had the time and no toddler, I could figure out the average time it would take you to pair up all the socks (someone has surely already done this). This doesn't even take into account all the lone socks that simply have no mate, no matter how many times you reach into the bin. I realize that in real life the grabs are not random (you won't accidentally grab Eleanor's purple soc...

Eleanor's cousin introduced her to the "dot" game: you take a grid with dots, each person draws a line connecting two adjacent dots (north, south, east or west), and if you draw the fourth line creating the square you write your initial in it and go again. Here's the wikipedia article, if you're interested. Eleanor drew her own (slightly wobbly) grid with 100 squares. She was quite impressed with the grid and she was convinced that her mother would much rather play dots with her than clean the kitchen. I actually felt as though I had paid my dues playing the dots and boxes game when I was younger, but I started playing just to spend time with her. I was expecting to be bored, try to help her win, and go back to cleaning. Almost immediately Eleanor decided we should change the rules for the game. Now you didn't have to connect adjacent dots, you could connect any dots, as long as you didn't go through another dot or cross another line. When you compl...

One of the downsides of having kids is that all of the things you hate dealing with for yourself you now get to deal with for 3 (in my case) more people. For example, one of my least favorite tasks is sorting socks. I dislike it so much that as soon as the frost is off the ground in the spring, I get out my sandals, which I wear until my toes start freezing. Soon after Michael and I married we made an arrangement whereby I would not have to sort and fold his socks. Now I get to keep track of and sort Amanda's and Eleanor's socks. It wouldn't be so bad except that as soon as they have been worn once, one of the socks seems to disappear into the ether (the hozone, Michael always says). Here's a math question for the audience: if you have 10 pairs of socks in a pile, and you reach in to the pile and grab a random pair, how many do you have to grab before you have a pair? (at least 2, at most 11, and I think it follows some sort of normal distribution, I think...) I...