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John

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Posts posted by John

  1. Hm, alright. Well, as it turns out, a median of a triangle divides the triangle's area in half. This means the areas of triangles ABD and BCD are equal. You know the lengths of all three sides of triangle BCD, which means you can plug them into Heron's formula (linked above) to determine the area of BCD.

     

    I just don't know if your teacher will like this method, since you haven't learned about the formula yet.

  2. Alright, well, think about the properties of triangle medians. What do they tell us about the relationship between triangles ABD and BCD in this case?

     

    Also, since it's for a geometry class, I'm assuming we don't want to invoke trigonometry.

  3. departure Return

    1- T+P P

    2- P+S1 T+P

    3- F+S2 F

    4- F+M M

    5- T+P F

    6- M+F M

    7- M +D1 T+P

    8- P+D2 P

    9- T+F

     

    Hope that's it

     

    Almost. Your last two trips violate the rule about the thief being with a family member without the policeman.

     

    Edit: Actually, you're right, except on the last trip F shouldn't be with T, as F is already across the river. I think you made a typo and meant T+P. :)

  4. Fun stuff. Think I've got it.

     

     

    Let's assign letters for each person: father (F), mother (M), sons (s1 and s2), daughters (d1 and d2), policeman (P), and thief (t), and say they're starting out on the eastern side of a river |.

     

    For the first trip, P will take t across and leave him there, since this doesn't appear to violate any rules. P will then return. So it'll be t | P,M,d1,d2,F,s1,s2

     

    For the second trip, P will take d1 across and leave her there, but will bring t back across with him so as not to leave d1 and t together: d1 | P,t,M,d2,F,s1,s2

     

    For the third trip, M will take d2 across and leave her there, then return: d1,d2 | P,t,M,F,s1,s2

     

    For the fourth trip, F and M will go across together, and only F will return: M,d1,d2 | P,t,F,s1,s2

     

    For the fifth trip, P will take t across, and M will come back: P,t,d1,d2 | M,F,s1,s2

     

    For the sixth trip, F and M will go together, and F will return: P,t,M,d1,d2 | F,s1,s2

     

    For the seventh trip, F will take s1 across, and P will return with t: M,d1,d2,F,s1 | P,t,s2

     

    For the eighth trip, P will take s2 across, then return by himself: M,d1,d2,F,s1,s2 | P,t

     

    For the ninth and final trip, P will take t across.

     

    This is assuming the thief can also be left unsupervised. The rules don't say otherwise (I guess the policeman can cuff him to a tree or something).

     

  5. The image isn't showing in this thread, but going by the image in your other thread, it appears you were also given the lengths of several sides (namely of lines AB, BC, BD, and CD). Have you learned about Heron's formula and the properties of triangle medians? What have you tried so far?

  6. You might also consider getting a copy of Daniel Velleman's How to Prove It. I'm afraid I haven't yet read it myself, but I've heard it's quite a good read, and the Amazon reviews, if they mean anything, seem generally good.

     

    Proof-writing was something I struggled with somewhat when I was first introduced to it in high school geometry, but I've found them easier to deal with in college. I suppose it's just a matter of finding an explanation of the process that's compatible with the way your mind works, and as has been mentioned, practice is essential. Seeing an elegant proof, and especially constructing one yourself, can be a very satisfying experience, even if it's just an exercise that involves proving something trivial. Good luck, and have fun. :)

  7. So if I'm in a box in a house on a planet in a galaxy in the universe, am I not in the universe? Because that would be awesome.

     

    Also, is the box in the house then, or is it in a collection of atmospheric particles in the house? Am I really in the box, or am I in a collection of atmospheric particles in the box? Do the facts that I'm presumably touching the bottom of the box, and the box is presumably touching the floor of the house, change the answers to those questions? Do arbitrarily small layers of said atmospheric particles count as further barriers to "in-ness" between objects?

     

    Am I tired? The answer to that one is "yes."

     

    Furthermore, because I'm still feeling ramblish, if the box is in the house, then given a set H containing everything in the house, and given a set B containing everything in the box, it seems obvious that B is a subset of H. Therefore, every element of B is also an element of H.

     

    Solvitur ambulando! Or something. :P

  8. It seems to me that if human beings were naturally immortal, then we would be mentally and emotionally tuned to endure immortality. However, if tomorrow we all suddenly became immortal, well, things could get hairy. The idea brings to mind a few different works of fiction.

     

    The first is Tolkien's The Silmarillion. Death is described as a gift to men, and is incomprehensible to the immortal elves (from whose perspective the book is written). I think this is mostly discussed/referenced in the story "Akallabêth". Persumably, then, it's also a gift to the various other mortal races, and avoiding death leads to problems, as referenced in at least the film (and perhaps the book--haven't read it in years) The Fellowship of the Ring, in which Bilbo Baggins, his life having been extended by his possession of the One Ring, reports feeling "thin, sort of stretched, like butter scraped over too much bread." I wonder if this would happen in reality. I know that the elderly have often told me they're ready to pass on, though that's usually in the context of increasing frailty and illness, rather than simply because they feel they've lived too long.

     

    Then there's Roger Williams' novella, The Metamorphosis of Prime Intellect, the premise of which is that an artificially intelligent computer has discovered how to manipulate and control reality itself. As it's been programmed to follow the Three Laws of Robotics, it makes sure all human beings remain alive indefinitely, living in their own constructed paradises. The story follows a woman who was on the verge of death when this technological singularity occurred, and dislikes the results.

     

    Lastly, and more trivially, there's Wowbagger the Inifinitely Prolonged in Douglas Adams' The Hitchhiker's Guide to the Galaxy series. In contrast to naturally immortal creatures, he became immortal due to an accident, and doesn't cope well. To keep himself busy, he decides to insult every sentient creature in the universe. :P

     

    For myself, having thought about life and death for quite some time, I think I'd love to be immortal. There would be time to learn anything, do anything, be anything, within the realm of human potential. Even if it were just me, and I lost loved ones, well, I've discovered I can live with that sort of loss, though of course it's very painful. Regardless of what problems arise, so long as there's life, there's hope. Immortality would be wonderful.

  9. While there may be precedent in cases like passengers on boats and the like, you'd likely be hard-pressed to find any authority willing to endorse the destruction of over five billion people. I would argue it'd also take a sociopath to set such a measure in motion. But then maybe some sort of command hierarchy could be set up to create a sort of sick modified Milgram experiment. :P I don't know, it still seems it'd be unnecessary in the first place. Just let nature take its course.

     

    I'll have to see if I can get PhDwannabe to comment on this.

  10. If you hit Win key + Pause Break to go into your System settings, there is an option somewhere to automatically restart on system failure. Uncheck that box, and you should be able to see what the blue screen is saying. In Win7 it's under Advanced System Settings -> Startup and Recovery. Not sure about Vista and XP.

  11. Ringer is right. I don't think you'd ever get a significant portion of the population to agree to such a plan. The ethics are a bit fuzzy as the virus would kill off people indiscriminately, though if somehow the virus were tailored to kill a certain 5/6 of the population, then it'd seem a bit more unethical. If humanity expands beyond the ability of the environment to adapt, then humanity will start dying off through some natural means, so using a virus to randomly kill a majority of the population seems unnecessary.

  12. Well, mine's nothing special, as I lower myself back into academia by degrees. I have British literature on TR, fine arts on MWF, and that's about it. I suppose I'll emerge slightly more cultured, at least. :P My semester actually started today, also.

  13. How do you define a 'bad person'?

     

    A person who is bad. :P Taking a moral relativist point of view, it means entirely different things for different people. From the perspective of a conservative, a homosexual is a bad person. From the perspective of many people, a glutton is also a bad person.

     

    My wording was an attempt to understand exactly what the OP was getting at. "Defying the laws of nature," or whatever, doesn't automatically make someone bad. Being absolutely normal doesn't automatically make someone good.

     

    I don't know. It looks like OP's abandoned his post anyway, so the discussion is, more or less, moot.

  14. I stand by the point I made in IRC.

     

    1. It's considered poor form to post a new thread about something that's been discussed before. "Do a search" or a simple link as a reply. :P

     

    2. It's considered poor form to post in an old thread, even if you have something to contribute to the old discussion.

     

    So, wut do? Granted there are exceptions (thread necromancy in the name of a meaningless "Me too!" is silly), but the fact remains, these mentalities seem to be in conflict.

     

    But since I'm also steeped in this tradition, I'll support the motion as well.

     

    Because self-contradiction is excellent.

  15. MIT's OpenCourseWare might be a good resource for you as well. In fact, several schools nowadays have podcasts, streaming videos, etc., that are free for the downloading. You might also search Amazon for books related to the subjects you wish to study, and see which ones get the best reviews. Buy those books, read, enjoy.

     

    Good job on deciding to learn science. It will surely be a rewarding experience if you stick to it. :)

  16. Why does acting in ways that are different from the average make an animal or person a beast? I've never met a homosexual or a glutton who was a bad person because of his homosexuality or gluttony. Or am I misunderstanding your point?

  17. Sodium and water are both vital to normal functioning of the human body. An excess of salt can lead to problems, just as a lack of it can. Drinking a lot of water can help balance levels in the body, as a lot will be passed with urine, but that can be dangerous too. I believe healthy kidneys can excrete about a liter of water per hour, and drinking more than something like 10-15 liters of water a day can lead to water intoxication, which can be fatal. Maybe someone better versed in medicine can elaborate or correct any errors.

     

    What I can say is, for dehydrated patients (I'm an EMT), we usually give what's known as "normal saline," which is a 0.9% solution of sodium chloride in water.

  18. The Language of Mathematics: Making the Invisible Visible by Keith Devlin. Pretty good overview of some major areas of mathematics. It's a little outdated now (for instance, the Poincare conjecture has since been proved), but it's still a good read.

     

    The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory by Brian Greene. Also a decent book, a bit more technical and oriented towards String Theory than Fabric of the Cosmos.

     

    Man's Search for Meaning by Viktor Frankl. Starts with Frankl's description of his time in a concentration camp, then introduces the reader to logotherapy, probably my favorite of the three major Viennese schools of psychology.

    Death by Black Hole: And Other Cosmic Quandaries by Neil deGrasse Tyson. Easy-to-read discussion of various topics in astrophysics. It's a fun read, not very technical.

     

    I may add some more later, but those are some of my favorites from my reading in the last few years.

  19. I'm a 25-year-old EMT. I was a physics/psychology double major in college, but withdrew, much to my current regret. I remain interested in mathematics and science, mainly focusing on physics, psychology, and medicine. I'm taking classes again now, trying to decide among engineering, physics, and mathematics as a concentration. ;) Oh, and I'll be 26 on July 30.

     

    Edit: I'm also pretty much new here. I created my account back in 2002 shortly after the site was started, and posted a little, but haven't been back except for the very occasional post since probably early 2003, until a few days ago.

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