I've always thought of it like a "science" based on logic. It is a quest to discover "truth", not an invention. I have a hard tome with some who feel that scientists are some kind of atheists whose goal is to disprove religion. I don't think of theologies as anti-science or science as anti-theologies. Oops.....I got of on a tangent (getting back to math). I haven't watched the linked video yet, though..
Tom Adams, post: 375189, member: 7285 wrote: I've always thought of it like a "science" based on logic. It is a quest to discover "truth", not an invention. I have a hard tome with some who feel that scientists are some kind of atheists whose goal is to disprove religion. I don't think of theologies as anti-science or science as anti-theologies. Oops.....I got of on a tangent (getting back to math). I haven't watched the linked video yet, though..
Instead of a nap sometime view RJ's link to the NPR program.
Viewed it last summer as part of our 12 yr old's summer math home study. He was already familiar with the Fibonacci Sequence to my surprise.
There is no definitive of course.
This summer , we are going to study solid geometry. Oh boy! Gonna get all kind of Greek with him.
Formulas for circumference and volumes of cones, triangles, polyhedrons, cylinders etc.
But he just finished 7th grade last week, so he has a few weeks to fish, play soccer, bike, kayak, and hang out.
Maybe at the end of the summer, we will dissect one of his old "truncated icosahedrons" that are about and work some math..
Robert Hill, post: 375194, member: 378 wrote: Instead of a nap sometime view RJ's link to the NPR program.
I'll definitely check it out.
paden cash, post: 375133, member: 20 wrote: Math is an approximation of physical properties (truths). No trig functions, excluding 0å¡ and 90å¡ are finite. ëÊ (Pi) is not a finite number...they are approximations. ..;-)
The sine of 30 degrees is 1/2 and the tangent of 45 degrees is 1. Now pi, like the square root of 3, is an irrational number, but a number nonetheless. If you solve the equation x*sqrt(3) = 3, the answer is sqrt(3). And the exact area of a circle with radius = 3 is 9pi.
But it's hard to buy exactly sqrt(3) gallons of paint or determine the exact amount of paint that will cover a circle with a radius of 9pi. Arithmetic has trouble with irrational numbers but mathematics does not.
Complex, irrational, rational, integer, or natural, they're all numbers. Whether they're discovered or created, they all contribute and help us understand the world around us.
MathTeacher, post: 375212, member: 7674 wrote: The sine of 30 degrees is 1/2 and the tangent of 45 degrees is 1. Now pi, like the square root of 3, is an irrational number, but a number nonetheless. If you solve the equation x*sqrt(3) = 3, the answer is sqrt(3). And the exact area of a circle with radius = 3 is 9pi.
But it's hard to buy exactly sqrt(3) gallons of paint or determine the exact amount of paint that will cover a circle with a radius of 9pi. Arithmetic has trouble with irrational numbers but mathematics does not.
Complex, irrational, rational, integer, or natural, they're all numbers. Whether they're discovered or created, they all contribute and help us understand the world around us.
I agree, whole-heartedly. And thank you for differentiating arithmetic and mathematics.
But just 'cause I like arguing (as pointed out by a frustrated trig professor long ago)...as a surveyor, I am forced to deal in rational concepts. It is very difficult to explain to a City Council (that is weighing an approval of a permit due to area) that the area is something along the lines of pi(R squared)....or the length of line has something to do with 1 over the square root of 3. I deal in a world that wants rational explanations. And rational is not always exact.
good point
Just because we can not find an exact solution with our finite minds does not mean an exact answer does not exist. An atheist is simply a dishonest or unenlightened agnostic. We have an error ellipse because our system of measurement does not account for all factors. Some of the factors have yet to be discovered.
lmbrls, post: 375220, member: 6823 wrote: Just because we can not find an exact solution with our finite minds does not mean an exact answer does not exist. An atheist is simply a dishonest or unenlightened agnostic. We have an error ellipse because our system of measurement does not account for all factors. Some of the factors have yet to be discovered.
A few years ago I had a real estate broker contact me to inquire about a description I wrote that he felt "did not close". OK, lemme look that up...
I say it does. He said it doesn't. By how much I asks....the "mis-closure" was in the thousandths...
Now I dummy down my line labeling to degrees minutes and seconds...and lengths to the hundredths. After a phone discussion with him about his software we determined he too could fix his units to not read out to six or seven places. I explained our minimum standards were only to the arc second with distances to the hundredth of a foot.
He called me back shortly and told me everything was fine. I'm glad we've got folks watching us to make sure we "do it right"...
Tom Adams, post: 375198, member: 7285 wrote: I'll definitely check it out.
Oops I meant PBS
paden cash, post: 375217, member: 20 wrote: I deal in a world that wants rational explanations. And rational is not always exact.
Very well said. One of the things that made teaching fun was the opportunity to delve into some of the pure math things. One of the other things that made it fun was delving into the real-world applications.
One of my favorite reads and re-reads is "The Pleasure of Finding Things Out" by Dr. Richard Feynman. From Los Alamos through to the Nobel Prize and on to the space shuttle Challenger disaster, Dr. Feynman was both theoretician and practical man. And he was a difficult person for authority to control.
In fact, I think I'll take it to the beach again this summer.
[MEDIA=youtube]FdYKTek5N1Q[/MEDIA]
Robert Hill, post: 375224, member: 378 wrote: Oops I meant PBS
I watched the linked video. It's good.
MathTeacher, post: 375227, member: 7674 wrote: Very well said. One of the things that made teaching fun was the opportunity to delve into some of the pure math things. One of the other things that made it fun was delving into the real-world applications.
One of my favorite reads and re-reads is "The Pleasure of Finding Things Out" by Dr. Richard Feynman. From Los Alamos through to the Nobel Prize and on to the space shuttle Challenger disaster, Dr. Feynman was both theoretician and practical man. And he was a difficult person for authority to control.
In fact, I think I'll take it to the beach again this summer.
I prefer Feyman's "Surely you're joking Mr Feynman." He was a unique individual who recognized that much of what people claim to understand is mere repetition of what they have been told. I also recommend his "What do you care what other people think?" And "Perfectly reasonable deviations..."
For those with more serious interests do a search for his books. Many good insights. I found that his classic Caltech project to rethink how to teach physics to undergraduates, realized in the three volume "The Feyman Lectures on Physics" originally published in 1964 is available for free viewing here:
Dr. Feynman was one of a kind alright. I like the Los Alamos experience and the Challenger inquiry in "The Pleasure...." But "Surely You're Joking..." and the others are great reads as well.
Did you see "The Big Bang Theory" episode where the boys acquired Dr. Feynman's VW bus?
Did not see the show but forgot to mention his notation for interactions in particle physics (Feynman diagrams) where ..."the physical content of the theory is (more) intuitively understood by looking at the diagrams directly and ignoring the math." The last half of the first sentence was modified from : http://www.quantumdiaries.org/2010/02/14/lets-draw-feynman-diagams/
My suggestions are good summer reads (light and accessible). His recorded lectures were in heavy rotation on road trips years ago.
I have seen the TV show but find it perpetuates the stereotype of socially inept scientists and engineers. I also lack a sense of humor.
I share your take on Big Bang Theory. It's pretty much overdone at this point and it does portray scientists in a bad light.
"Scorpion" had promise, but it seems so contrived. And the athletic feats that those non-athletic nerds perform each week are pretty much impossible.
I'll take Feynman's writings any day.
