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  • 0 posts edited
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  • 27 votes cast
May
19
awarded  Citizen Patrol
May
19
comment If you draw two cards, what is the probability that the second card is a queen?
@Tony - If the first card is an ace, then it is less likely that the 2nd card is an ace. From a card player's perspective, that's true. But, what happens when the first card is not an ace? Then, it is more likely that the second card is an ace. 1/13th of the time the probability will go down, while 12/13ths of the time the probability will go up. In the end, the numbers cancel out, and we're back to 1/13th. A.J.'s answer has the actual values.
Feb
22
comment Visually stunning math concepts which are easy to explain
@Peter - I'll admit that I'm using the word derive a bit loosely for a mathematics forum (it's a soft answer to a soft question), but it's too bad you see this as "dumbing down" and "a waste of time." Most 7th-grade teachers charged with teaching volume would simply write the formula on the board, and it would be well-forgotten by the end of summer. Her technique might have been weak insofar as mathematical rigor goes, but the pedagogy was very strong. I assure you, this woman was not one to "dumb down" anything; I remember re-learning concepts in 11th-grade that she taught us in Jr High.
Feb
15
awarded  Great Answer
Dec
19
awarded  Constituent
Dec
15
awarded  Caucus
Oct
19
comment Does $1.0000000000\cdots 1$ with an infinite number of $0$ in it exist?
RE: "I think there is only one infinity, we can think it as the biggest number..." You might want to get a better grasp on what infinity means; there is no "biggest number." Incidentally, a better way to phrase your title would be to refer to the string of 0's as infinitely many zeroes, not an infinite number of zeroes.
Sep
24
awarded  Autobiographer
Aug
28
comment Visually stunning math concepts which are easy to explain
@DanielM - You're right, the experiment isn't a proof. Then again, neither is the formula. I just wanted to draw attention to how my math teacher's technique left a lasting impression that the formula by itself could never manage to do.
Apr
22
revised If there are obvious things, why should we prove them?
deleted 1 character in body
Apr
20
answered If there are obvious things, why should we prove them?
Apr
20
comment If there are obvious things, why should we prove them?
Not my downvote, either, but: Immoral? Sacred? For someone professing such strict adherence to rigor, those words are a bit over-the-top.
Apr
20
comment Are there 3 trig functions or are there 6 trig functions?
The bottom line answer always seems to be "it depends." Great link, btw.
Apr
13
comment Visually stunning math concepts which are easy to explain
@Travis - That's why I gave up and constructed my own image. (Hopefully one that illustrates my point a little better.) I left the other image in my answer so as not to render all these comments obsolete.
Apr
13
awarded  Editor
Apr
13
revised Visually stunning math concepts which are easy to explain
added 411 characters in body
Apr
13
comment Visually stunning math concepts which are easy to explain
@Travis - Yes, a few folks have made that observation. Perhaps I didn't choose the best examples. I'll stand by my point, though: diagrams showing little more than a polygon, some labels, and an equation often lead a student toward a plug-and-chug mindset that isn't as instructive as it could be. I still think first diagram has plenty of room for improvement; it could be drawn in a way that would do a better job of nudging a student toward your line of reasoning.
Apr
7
awarded  Good Answer
Apr
7
comment Visually stunning math concepts which are easy to explain
@LaC - I'd think the first picture would be fine, too, if it had a rectangle drawn around it, so that it's plain to see that the four triangles that form the rhombus cover half the rectangle. My beef with the first drawing is that most middle schoolers would not think to do that; I'm afraid they'd simply follow the formula without any thought about why it works.
Apr
7
awarded  Nice Answer