http://www.scientificamerican.com/article.cfm?id=fact-or-fiction-living-outnumber-dead&ref=sciam
The human population has swelled so much that people alive today outnumber all those who have ever lived, says a factoid whose roots stretch back to the 1970s.
Tuesday, December 1, 2009
Thursday, November 19, 2009
Math Day
I took some kids from my school down to CSU-Pueblo for a math competition today and our upperclassmen did very well. We lost to only one team and came home with a big trophy for the math bowl competition. In the individual written contest, we got a 2nd place, 5th place, and two honorable mentions - so all our upperclassmen placed. We did the best out of all the schools in our district that went down on the bus together to the competition.
The pictures in this post were taken at the CSU-Pueblo Physics/Math building - they had some neat art reminiscent of Islamic tilings.
Wednesday, July 8, 2009
Math Humor
One evening Rene Descartes went to relax at a local tavern. The tender approached and said, "Ah, good evening Monsieur Descartes! Shall I serve you the usual drink?". Descartes replied, "I think not.", and promptly vanished.
---
"The problems for the exam will be similar to the ones discussed in the class. Of course, the numbers will be different. But not all of them. Pi will still be 3.14159... "
---
Salary Theorem
The less you know, the more you make.
Proof:
Postulate 1: Knowledge is Power.
Postulate 2: Time is Money.
As every engineer knows: Power = Work / Time
And since Knowledge = Power and Time = Money
It is therefore true that Knowledge = Work / Money .
Solving for Money, we get:
Money = Work / Knowledge
Thus, as Knowledge approaches zero, Money approaches infinity, regardless of the amount of Work done.
---
Pi goes on and on and on ...
And e is just as cursed.
I wonder: Which is larger
When their digits are reversed?
---
Abbott and Costello made arithmetic shenanigans the basis
of a number of their comic dialogs.
Here is a dialog from their movie titled Buck Privates:
Abbott: You're 40 years old, and you're in love with a little girl,
say 10 years old. You're four times as old as that girl.
You couldn't marry that girl, could you?
Costello: No. ?
Abbott: So you wait 5 years. Now the little girl is 15, and you're 45.
You're only three times as old as that girl.
So you wait 15 years more.
Now the little girl is 30, and you're 60.
You're only twice as old as that little girl. ?
Costello: She's catching up. ?
Abbott: Here's the question. How long do you have to wait before you
and that little girl are the same age?
Costello: What kind of question is that? That's ridiculous.
If I keep waiting for that girl, she'll pass me up.
She'll wind up older than I am.
Then she'll have to wait for me!
Here's another encounter from Buck Privates, one echoed in
several later movies.
Abbott: Do me a favor. Loan me $50.
Costello: I can't lend you $50. All I've got is $40.
Abbott: That's okay. Give me the $40, and you'll owe me $10.
Costello: How come I owe you $10?
Abbott: What did I ask you for?
Costello: $50.
Abbott: What did you give me?
Costello; $40.
Abbott: So you owe me $10.
Costello: That's right. But you owe me $40. Give me my $40 back.
Abbott: There's your $40. Now give me the $10 you owe me.
That's the last time I'll ever ask you for the loan of $50.
Costello: How can I loan you $50 now? All I have is $30.
Abbott: Give me the $30, and you’ll owe me $20.
Costello: This is getting worse all the time.
First I owe you $10, and now I owe you $20!
Abbott: So you owe me $20. Twenty and 30 is 50.
Costello; Nope! Twenty-five and 25 is 50.
Abbott: Here's your $30. Give me back my $20.
Costello: All I've got now is $10!
Abbott then entices Costello into a silly, double-or-nothing
number game.
Abbott: Take a number, any number at all from 1 to 10, and don't tell me.
Costello: I got it.
Abbott: Is the number odd or even?
Costello: Even.
Abbott: Is the number between 1 and 3?
Costello: No.
Abbott: Between 3 and 5?
Costello: No. I think I got him.
Abbott: Between 5 and 7?
Costello: Yes.
Abbott: Number six?
Costello: Right. . . . How did he do that?
Toward the end of the movie, during a boxing match, Costello is
knocked to the canvas, and the biased referee gives a quick
count: 2, 4, 6, 8, 10.
Costello: What's this? 2, 4, 6, 8, 10? What happened
to 1, 3, 5, 7, and 9?
Ref: I don't like them numbers. They're odd.
X equals just about everything I learned of math in school
By DAVE BARRY
--------------------------------------------------------------------------------
President Bush says our schools need to do a better job of teaching mathematics, and I agree with him 150 percent. Many high-school students today can't even calculate a square root! Granted, I can't calculate a square root, either, but I USED to be able to, for a period of approximately 15 minutes back in 1962. At least I think that was a square root. It might have been a ``logarithm.''
But whatever it was, if I had to learn how to do it, these kids today should have to learn it, too. As President Bush so eloquently put it in his address to Congress: ``Mathematics are one of the fundamentaries of educationalizing our youths.''
I could not have said it better with a 10-foot pole. We all need mathematics in order to solve problems that come up constantly in the ``real world.'' For example, suppose four co-workers go to a restaurant, and at the end of the meal, the waiter brings a bill totaling $34.57. How much, including tip, does each person owe? If the co-workers do not know mathematics, they will just guess at the answer and put in random amounts of money ranging from $9 to $11, unless one of them is a guy I used to work with named Art, in which case he will make a big show of studying the bill, then put in exactly $4.25.
But if the co-workers know their mathematics, they can easily come up with EXACTLY the correct answer. They can do this using ``algebra,'' which was invented by the ancient Persians. (They also invented the SATs, although they got very low scores because in those days there were no pencils.) The way algebra works is, if you don't know exactly what a number is, you just call it ``X.''
The Persians found that this was a BIG mathematical help in solving problems:
PERSIAN WIFE (suspiciously): How much have you had to drink?
PERSIAN HUSBAND: I had ``X'' beers.
PERSIAN WIFE: Well, how much is THAT?
PERSIAN HUSBAND: It's a (burp) variable.
PERSIAN WIFE (not wanting to look stupid): Well, OK then.
Historical Footnote: Several years later, when the ancient Romans invented Roman numerals, and it turned out that ``X'' was actually equal to 10, there was BIG TROUBLE in Persia.
But getting back to the four co-workers at the restaurant: To figure out how much each person owes, they would simply use the algebraic equation AEPO=1/4$34.57+T(((-SA?)@
(+NSOB!)(-SITE)(H), where ``AEPO'' is the amount each person owes, ``T'' is the tip, ``SA'' is whether the waiter has a snotty attitude, ``NSOB'' is whether the waiter has a nice set of buns, ``SITE'' is a variable used if you think somebody in the kitchen is spitting in the entrees, and H is hydrogen. Using this equation, our four co-workers can easily calculate that each one owes exactly, let's see... carry the 7... OK, it would probably be somewhere between $9 and $11.
So we see that algebra is a vital tool for our young people to learn. The traditional method for teaching it, of course, is to require students to solve problems developed in 1928 by the American Association of Mathematics Teachers Obsessed With Fruit. For example:
``If Billy has twice as many apples as Bobby, and Sally has seven more apples than Chester, who has one apple in each hand plus one concealed in his knickers, then how many apples does Ned have, assuming that his train leaves Chicago at noon?''
The problem is that these traditional algebra problems are out of date. Today's young people are dealing with issues such as violence, drugs, sex, eating disorders, stress, low self-esteem, acne, global warming and the demise of Napster. They don't have time to figure out how many apples Ned has. If they need to know, they will simply ASK Ned, and if he doesn't want to tell them, they will hold him upside down over the toilet until he does. And then Ned will sue them, plus the school, plus his parents for naming him ``Ned'' in the first place. Ultimately the ACLU will get the Supreme Court to declare that the number of apples a student has is protected by his constitutional right to privacy.
So what is the solution? How do we balance our children's need to learn math against the many other demands placed on them by modern life? I believe there IS a solution, one that is both simple and practical. I call it: ``X.''
---
"The problems for the exam will be similar to the ones discussed in the class. Of course, the numbers will be different. But not all of them. Pi will still be 3.14159... "
---
Salary Theorem
The less you know, the more you make.
Proof:
Postulate 1: Knowledge is Power.
Postulate 2: Time is Money.
As every engineer knows: Power = Work / Time
And since Knowledge = Power and Time = Money
It is therefore true that Knowledge = Work / Money .
Solving for Money, we get:
Money = Work / Knowledge
Thus, as Knowledge approaches zero, Money approaches infinity, regardless of the amount of Work done.
---
Pi goes on and on and on ...
And e is just as cursed.
I wonder: Which is larger
When their digits are reversed?
---
Abbott and Costello made arithmetic shenanigans the basis
of a number of their comic dialogs.
Here is a dialog from their movie titled Buck Privates:
Abbott: You're 40 years old, and you're in love with a little girl,
say 10 years old. You're four times as old as that girl.
You couldn't marry that girl, could you?
Costello: No. ?
Abbott: So you wait 5 years. Now the little girl is 15, and you're 45.
You're only three times as old as that girl.
So you wait 15 years more.
Now the little girl is 30, and you're 60.
You're only twice as old as that little girl. ?
Costello: She's catching up. ?
Abbott: Here's the question. How long do you have to wait before you
and that little girl are the same age?
Costello: What kind of question is that? That's ridiculous.
If I keep waiting for that girl, she'll pass me up.
She'll wind up older than I am.
Then she'll have to wait for me!
Here's another encounter from Buck Privates, one echoed in
several later movies.
Abbott: Do me a favor. Loan me $50.
Costello: I can't lend you $50. All I've got is $40.
Abbott: That's okay. Give me the $40, and you'll owe me $10.
Costello: How come I owe you $10?
Abbott: What did I ask you for?
Costello: $50.
Abbott: What did you give me?
Costello; $40.
Abbott: So you owe me $10.
Costello: That's right. But you owe me $40. Give me my $40 back.
Abbott: There's your $40. Now give me the $10 you owe me.
That's the last time I'll ever ask you for the loan of $50.
Costello: How can I loan you $50 now? All I have is $30.
Abbott: Give me the $30, and you’ll owe me $20.
Costello: This is getting worse all the time.
First I owe you $10, and now I owe you $20!
Abbott: So you owe me $20. Twenty and 30 is 50.
Costello; Nope! Twenty-five and 25 is 50.
Abbott: Here's your $30. Give me back my $20.
Costello: All I've got now is $10!
Abbott then entices Costello into a silly, double-or-nothing
number game.
Abbott: Take a number, any number at all from 1 to 10, and don't tell me.
Costello: I got it.
Abbott: Is the number odd or even?
Costello: Even.
Abbott: Is the number between 1 and 3?
Costello: No.
Abbott: Between 3 and 5?
Costello: No. I think I got him.
Abbott: Between 5 and 7?
Costello: Yes.
Abbott: Number six?
Costello: Right. . . . How did he do that?
Toward the end of the movie, during a boxing match, Costello is
knocked to the canvas, and the biased referee gives a quick
count: 2, 4, 6, 8, 10.
Costello: What's this? 2, 4, 6, 8, 10? What happened
to 1, 3, 5, 7, and 9?
Ref: I don't like them numbers. They're odd.
X equals just about everything I learned of math in school
By DAVE BARRY
--------------------------------------------------------------------------------
President Bush says our schools need to do a better job of teaching mathematics, and I agree with him 150 percent. Many high-school students today can't even calculate a square root! Granted, I can't calculate a square root, either, but I USED to be able to, for a period of approximately 15 minutes back in 1962. At least I think that was a square root. It might have been a ``logarithm.''
But whatever it was, if I had to learn how to do it, these kids today should have to learn it, too. As President Bush so eloquently put it in his address to Congress: ``Mathematics are one of the fundamentaries of educationalizing our youths.''
I could not have said it better with a 10-foot pole. We all need mathematics in order to solve problems that come up constantly in the ``real world.'' For example, suppose four co-workers go to a restaurant, and at the end of the meal, the waiter brings a bill totaling $34.57. How much, including tip, does each person owe? If the co-workers do not know mathematics, they will just guess at the answer and put in random amounts of money ranging from $9 to $11, unless one of them is a guy I used to work with named Art, in which case he will make a big show of studying the bill, then put in exactly $4.25.
But if the co-workers know their mathematics, they can easily come up with EXACTLY the correct answer. They can do this using ``algebra,'' which was invented by the ancient Persians. (They also invented the SATs, although they got very low scores because in those days there were no pencils.) The way algebra works is, if you don't know exactly what a number is, you just call it ``X.''
The Persians found that this was a BIG mathematical help in solving problems:
PERSIAN WIFE (suspiciously): How much have you had to drink?
PERSIAN HUSBAND: I had ``X'' beers.
PERSIAN WIFE: Well, how much is THAT?
PERSIAN HUSBAND: It's a (burp) variable.
PERSIAN WIFE (not wanting to look stupid): Well, OK then.
Historical Footnote: Several years later, when the ancient Romans invented Roman numerals, and it turned out that ``X'' was actually equal to 10, there was BIG TROUBLE in Persia.
But getting back to the four co-workers at the restaurant: To figure out how much each person owes, they would simply use the algebraic equation AEPO=1/4$34.57+T(((-SA?)@
(+NSOB!)(-SITE)(H), where ``AEPO'' is the amount each person owes, ``T'' is the tip, ``SA'' is whether the waiter has a snotty attitude, ``NSOB'' is whether the waiter has a nice set of buns, ``SITE'' is a variable used if you think somebody in the kitchen is spitting in the entrees, and H is hydrogen. Using this equation, our four co-workers can easily calculate that each one owes exactly, let's see... carry the 7... OK, it would probably be somewhere between $9 and $11.
So we see that algebra is a vital tool for our young people to learn. The traditional method for teaching it, of course, is to require students to solve problems developed in 1928 by the American Association of Mathematics Teachers Obsessed With Fruit. For example:
``If Billy has twice as many apples as Bobby, and Sally has seven more apples than Chester, who has one apple in each hand plus one concealed in his knickers, then how many apples does Ned have, assuming that his train leaves Chicago at noon?''
The problem is that these traditional algebra problems are out of date. Today's young people are dealing with issues such as violence, drugs, sex, eating disorders, stress, low self-esteem, acne, global warming and the demise of Napster. They don't have time to figure out how many apples Ned has. If they need to know, they will simply ASK Ned, and if he doesn't want to tell them, they will hold him upside down over the toilet until he does. And then Ned will sue them, plus the school, plus his parents for naming him ``Ned'' in the first place. Ultimately the ACLU will get the Supreme Court to declare that the number of apples a student has is protected by his constitutional right to privacy.
So what is the solution? How do we balance our children's need to learn math against the many other demands placed on them by modern life? I believe there IS a solution, one that is both simple and practical. I call it: ``X.''
Tuesday, April 14, 2009
I love Logic Puzzles
I love Logic Puzzles, but they can be hard/frustrating at times!
Here is a simple (as in not complex, but as for easy or hard, I'll leave that up to you to decide)one to play - can you figure out how to always win this game?
Three Bags
How about this one?
Coin Weighing
Here is a simple (as in not complex, but as for easy or hard, I'll leave that up to you to decide)one to play - can you figure out how to always win this game?
Three Bags
How about this one?
Coin Weighing
Friday, February 13, 2009
A Nerdy Valentine's Gift for Those of You with TI Graphing Calculators
In Y =
Y1 = abs(x) + √(1 - x^2)
Y2 = abs(x) - √(1 – x^2)
In WINDOW
Xmin = -1
Xmax = 1
Ymin = -1
Ymax = 1.5
In FORMAT
AxesOff
In MODE
Simul
Y1 = abs(x) + √(1 - x^2)
Y2 = abs(x) - √(1 – x^2)
In WINDOW
Xmin = -1
Xmax = 1
Ymin = -1
Ymax = 1.5
In FORMAT
AxesOff
In MODE
Simul
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