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By Lydia_R · Posted
And I love your new profile pic @Ivy! Wow, looking great! -
By Jani · Posted
I hadn't heard about the John Sebastian invite. Interesting. He certainly would have blended in well with the other three. -
By Lydia_R · Posted
Thanks for responding @Vidanjali! You rock! Yes, I'm really good at trig and most of what you were writing about is old hat to me. I studied trig while I was living on the streets in 2004. After about two weeks of studying the Plane Trigonometry book that I had checked out from the Seattle library, I woke up at 3am on the sidewalk and realized that .5 is the sine of 30 degrees and .523 is the circumference measure in radians up to 30 degrees. After that, it all opened up for me and a few weeks later I coded an animated webpage slinky. I started getting into coding perspective properly. And then after a month or two of that, I went back to applying my new trigonometry skills to the collision detection I was coding previously only with ratios to make a video game I was calling Micropede, a Centipede type of clone. And then a few months after that I coded an Asteroids type clone with shields in about 4 hours that I called Bumper Bubbles. And with a bunch of effort of getting off of the streets and more studying, I went on to have a computer programming career for the last 20 years. I always get a kick out of getting paid to do trigonometry, but I'm certainly not doing it every day. This line of thought recently has come around to the old question of how to code the trigonometric function. What is the code inside of the multiplication, division and trig functions in a calculator? It seems that multiplication has the 10x10 multiplication table coded in as constants and then it loops to do numbers larger than 100 (for base 10). Division is just like how you would solve a division problem. It involves guessing. So a computer function to do division would have to go through loops while it guesses and uses multiplication. Then comes the trigonometric function. I've been thinking a lot lately that pi is calculated by producing a large physical wheel and rolling it out on a flat surface and measuring it. When I was on the streets, I would take a Starbucks stir stick and put a hole in either end of it. I'd put a push pin in one end and then my pen in the other end. That is one way to draw a perfect circle and it doesn't matter whether the stir stick is straight because the line between two points is always a perfect line. The other way to do it is with a string instead of the stir stick. When I was on the streets, it made me wonder how humans made perfectly straight, flat objects. My theory is that it evolved over time. Once you can create a perfect circle or saw blade, then you can use that to make a flat surface. But the trick is a crap in crap out deal. You have to start with a really perfect circle. But you have introduced a new concept here with the square root deal. Andy has been mentioning square roots with a song called the square root of two that he listens to. And that brings up irrational numbers and personally, with where I am at in math, I don't place a huge significance on "irrational" yet. I mean, would the same number have the same infinitely repeating pattern if it were expressed in a different base? Maybe it does. I don't tend to find the concept of that all too interesting. But how you mention sqrt(3)/2 is interesting and is something I haven't considered yet. You know, I could have been doing drugs on the streets, but I figured that I'd have a better chance at making a good life for myself if I studied this stuff and well, I was 33yo when I wound up on the streets and it's not like I felt I was missing out on some big drug experience that I hadn't experienced before. I got to the point where math and programming were more fun that drugs, so like that, I guess math became my drug of choice. Or work. Math is an inexpensive hobby. Hugs, Lydia_n -
By Abigail Genevieve · Posted
Right now I am more concerned about tornadoes than anything else, but then I am not all that concerned about tornadoes. If there is a watch or a warning I will take appropriate action. I take the precautions any woman takes when out in public in general. -
By Willow · Posted
@KymmieL yes you’d better avoid the Snap on Truck EXCEPT. (Oh oh) when you need a special tool. They are very good at having all the Dealerships only tools. They somehow get ahold of one (or made it in the first place) those things that keep dealers in that special place of being the only place certain things can be fixed. I once had a FiAT X1/9. Mid engine sports car. To adjust the timing, a relatively simple thing to do back in the 70s, you had two choices, cut a hole in the firewall to put a wrench through or buy or make a special wrench. Parts department at the dealer swore there was no such special wrench. After much research I found the part number. (Internet did not exist yet). It was before IBM made the first PC. The parts manager finally agreed to get me the part but only if I paid up front and it was mine, regardless of what came in. It was exactly what I needed a 14mm wrench with a specially shaped handle. That went around the distributor cap and turned backwards. Looked somewhat like the letter C with an open wrench head at the bottom. Fix It Again Tony -
By Ashley0616 · Posted
It depends on the circumstances. -
By atlantis63 · Posted
if I can eat it, sausages wrapped in bacon I say if I can eat it, I've been eating chocolate this afternoon.. lots of chocolate -
By Vidanjali · Posted
After I put on a binder I lie on my back on my bed and let gravity do its thing while I adjust the binder. This helps to make the chest flat and uniform. However its not perfect. If you have any sizeable chest, which I definitely do, there's going to be some bulge and I think that's unavoidable. But I have found letting the boobs drop off to the sides to be better than the mass of them being front and center. You will get some bulk along the sides, but I think that's easier to obscure with clothing and posture. Of course it helps to have a properly sized binder. The one you were given, is it too small or too big? If it's too big and if you have some sewing skills, you can try altering it. -
By Willow · Posted
Good morning it’s back to work today. Noon. Turned down another car. Yes it was everything they said it was but not exactly what I wanted. @awkward-yet-sweet you are right, when tools were made in the US like the Black and Decker/DeWalt line made in Baltimore or Rockwell Delta Milwaukee and so many others. But now they are all made in the same factories overseas using the same parts. It is really difficult to get good tools anymore. I am slowly switching any power tools to battery operated, but that also means you have to stick to one brand so that you don’t have lots of incompatible batteries and chargers. In some cases like DeWalt verses Black and Decker. I started with DeWalt so there I am. And now they are moving from 20v to 40v. Anything to keep you buying new. As for craftsman they always had a warrantied for for life and a line that wasn’t, they just didn’t tell customers that until you tried to get it replaced. My wrenches are all from before Sears went out and had a lifetime warranty but that is worthless now because it would be replaced the junk. Willow -
By Vidanjali · Posted
Oops don't know how that second diagram got in there at the end. Forgive the redundancy. -
By Vidanjali · Posted
I may be telling you things you already know, but I enjoy the discussion. The .523 is the angle measurement in radians. The .523 is actually a truncated irrational number (a number with infinitely long, nonrepeating decimal expansion). To six decimal places, it is 0.523599. Therefore, rounded to three decimal places, we actually have 0.524 as the 4th decimal place is 5 or greater. It is an irrational number because the conversion from degrees to radians entails the value pi which is irrational. The conversion is 30 X pi/180 because the angle measurement pi radians is equivalent to 180 degrees. If .577 were a rational number, you can read the decimal, "five hundred seventy seven thousandths" and then write the fraction, 577/1000. From there you would try to simplify the fraction, but this fraction does not simplify because 577 is a prime number (i.e. therefore, 577 and 1000 have no common factors to cancel). But .557 is also a truncated irrational number whose origin is tan(30 degrees) = 1/sqrt(3), where "sqrt" is an abbreviation for square root. It is irrational because sqrt(3) is irrational. (In fact, the square root of any prime number is irrational). Irrational numbers are so called because they cannot be expressed as the ratio of two integers. You can, however, acquire approximate values working with truncated irrational values such as .524 and .577. True that trig requires some memorization, but you can develop intuition as well. Do you understand trig in terms of the unit circle (circle with radius 1) centered at the origin of a rectangular coordinate system? And have you worked with calculations using angles measured in radians? This helps with visualization and makes memorization of values less critical. But it is critical to realize that most of the decimals which arise from trig calculations are irrational and their expressions are approximate. It is a lot of fun and indeed there are many applications in the arts. It's all about revolution and rotation. So is the concept of trig from the point of view of the unit circle. Consider how sundials were developed. Some time ago I watched a documentary series on ancient American civilizations and was impressed about their advanced knowledge of astronomy. There was one ancient site which was built like a sun dial. At specific hours of the day, the sun would align in such a way as to shine through specific constructions of the site creating stunning displays of symmetrical light and shadows. There were other sites where astronomical calendars were discovered showing the position of the sun during the solstices and equinoxes. In particular, this demonstrates the relationship between rotation of radius about a unit circle and the graph of the sine function which is a waveform. To reiterate, tan(30 degrees) = tan(pi/6 radians) = 1/sqrt(3) which is approximately equal to .577. And 30 degrees which is equivalent to pi/6 radians is approximately equal to 0.52359877559 which rounded to three decimal places is actually .524 (not .523). See if you can visualize this. Draw a set of axes, one vertical, the other horizontal. The point at which the axes cross is called the origin. Mark an arbitrary unit of 1 to the right, left, above, and below the origin on the axes. Now draw a circle whose circumference touches all four of those points. You have a unit circle. Now consider the radius of the circle which coincides with the right side of the horizontal axis as the base of a right triangle. Rotate the radius from its initial position counterclockwise by 30 degrees. Now drop a vertical line from that point on the circle and you have a right triangle with one angle of 30 degrees. It looks like this. tan(30 degrees) = length of opposite side / length of adjacent side. Well, we know the length of the hypotenuse of this triangle because we designed it using the unit circle. The coordinates noted on the above diagram give the cosine and sine of 30 degrees, respectively. Note that sine(30 degrees) = opposite/hypotenuse = (1/2)/1 = 1/2. cosine(30 degrees) = adjacent/hypotenuse = (sqrt(3)/2)/1 = sqrt(3)/2. And tan(30 degrees) = opposite/adjacent = (1/2)/(sqrt(3)/2) = 2/(2sqrt(3)) = 1/sqrt(3) which is approximately equal to .577 Sure enough. You just need to consider that you're working with approximations of irrational numbers. I suggest using the numbers as ratios involving pi. I believe you will have better results. It is fun stuff. -
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