Choose which operations are difficult

Post #225,395 by ben_tilly 9/18/05 11:02:59 PM Reply	Choose which operations are difficult Some of them have to be. Suppose that I go 30 miles, turn 45 degrees and go another 10. Where am I? The answer is an ugly number, and any method of calculation has to agree on that piece of ugliness. With usual trig, the ugliness lies in computing sin and cos. With his method, the ugliness lies in the difficulty of adding vectors. Knowing both approaches can be good because you get to choose the method that is more straightforward for the problem at hand. But neither is going to avoid the intrinsic issue that geometry doesn't always give nice numbers. Cheers, Ben I have come to believe that idealism without discipline is a quick road to disaster, while discipline without idealism is pointless. -- Aaron Ward (my brother)
Post #225,419 by Ashton 9/19/05 4:48:59 AM Reply	I'd have thought most folks can grok Pythagoras, at least - It is rather intuitive to complete the rectangle figure via the complementary triangle. In your sample, the diagram would need only a line and a triangle + a simple squares calculation. Is the answer 'ugly' because it's not an integer? (Maybe your example is just too practical and/or I've seen enough maps to be unable to tune out the 'visual' of what a 45\ufffd angle change means. Which would make me a lousy tutor for the algebra-only crowd, I guess :( Still, I also recall many people who didn't really grok that those trig 'names' are describing merely arithmetic ratios. And a few cases come to mind where the student could manage the flag-pole measurement via shadows from a nearby stick of known height ie A:B::C:D -- They may also have learned that simple manipulation by rote - not associating the idea of 'ratios' there either! as we would Wish they did. {sigh} It's hard to forget what one has gleaned. Yet teachers Must!
Post #225,519 by ben_tilly 9/19/05 6:23:22 PM Reply	Conceptually the problem is easy With standard trig, it is straightforward, you just have to know the sin and cos of 45 degrees. And the number comes out to be somewhat ugly. With the replacement for trig it isn't quite as straightforward. The "simple algebra" doesn't quite stay so simple. Cheers, Ben I have come to believe that idealism without discipline is a quick road to disaster, while discipline without idealism is pointless. -- Aaron Ward (my brother)
Post #225,553 by Silverlock 9/19/05 9:54:34 PM Reply	So this isn't bogus? I'm not enough of a math geek to understand on a cursory view if this is real or a con job. ----------------------------------------- George W. Bush and his PNAC handlers sent the US into Iraq with lies. I find myself rethinking my opposition to the death penalty. --Donald Dean Richards Jr.
Post #225,559 by ben_tilly 9/20/05 12:17:47 AM Reply	Somewhat Often you want to avoid explicit trig calculations. They are complex, slow, and introduce rounding errors. So having a way to think about trig that avoids them is useful. But push come to shove, there is inherent complexity that you aren't going to get around. Cheers, Ben I have come to believe that idealism without discipline is a quick road to disaster, while discipline without idealism is pointless. -- Aaron Ward (my brother)
Post #225,582 by drewk 9/20/05 9:31:36 AM Reply	Seems to me ... Trig is based on measurements of the triangle itself: what is the length of each side, what are the angles, etc. This method seems to enable doing formulas directly on the coordinates. I could be mis-reading -- okay, I didn't read the whole thing -- but that's what it looked like. === Purveyor of Doc Hope's [link\|http://DocHope.com\|fresh-baked dog biscuits and pet treats]. [link\|http://DocHope.com\|http://DocHope.com]

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