tag:blogger.com,1999:blog-5303307482158922565.comments2018-12-09T20:01:36.017-08:00Math Mama Writes...Sue VanHattumhttp://www.blogger.com/profile/10237941346154683902noreply@blogger.comBlogger2152125tag:blogger.com,1999:blog-5303307482158922565.post-85613453140099655742018-11-28T20:09:41.902-08:002018-11-28T20:09:41.902-08:00Newton-Raphson (which was known long before Newton...Newton-Raphson (which was known long before Newton or Raphson) makes figuring square-roots by hand not too bad. 192.7 is close to 14^2 (196), so the 2nd estimate would be 14 - (14^2-192.7)/28 = 14-33/280 = 3887/280. This turns out to be about 0.0005 off of the actual square root of 192.7. It converges quadratically, so the number of accurate digits roughly doubles with each iteration.<br /><br />I recently came across a problem that was of the form (1/log_a x) + (1/log_{a^2} x) + ... + (1/log_{a^k} x) = C, with the challenge to solve for x. That becomes much easier if you know the identity log_x y = 1/log_y x. The LHS becomes log_x a + log_x a^2 + ... + log_x a^k = log_x a^{1+2+...+k} = (k(k+1)/2) log_x a, which means that log_a x = k(k+1)/(2C). With proper choice of a, k and C this problem can look hard, but work out really easy.Buddha Buckhttps://www.blogger.com/profile/17167036913705912859noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-63385723784314749232018-10-29T19:49:29.585-07:002018-10-29T19:49:29.585-07:00I have never played these two games, but it sounds...I have never played these two games, but it sounds very interesting, maybe I will try it for Christmas.Melvin P. Orrhttps://www.tomtop.com/p-f1898.htmlnoreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-62966979790682320942018-09-11T18:38:33.865-07:002018-09-11T18:38:33.865-07:00Yes! I played at it years ago, and thought I menti...Yes! I played at it years ago, and thought I mentioned it in a post. But I don't find any previous mention of it on my blog. Thanks! I am playing now. The sciencevsmagic is smaller, and easier to conceive of finishing. I liked it better before. But this one is great too, and I just figured out the rhombus in a rectangle. Yay.Sue VanHattumhttps://www.blogger.com/profile/10237941346154683902noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-3078109228552256832018-09-11T15:49:23.564-07:002018-09-11T15:49:23.564-07:00Euclidea is also awesome.Euclidea is also awesome.mathematicamamahttps://www.blogger.com/profile/16356858870112804877noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-6917591349617978402018-09-09T20:24:45.360-07:002018-09-09T20:24:45.360-07:00My friend, Barbara, decided to try this in autocad...My friend, Barbara, decided to try this in autocad. She had trouble commenting. Here's what she says:<br /><br />I figured out how to construct a pentagram in AutoCad using only lines and circles (equiv. of straight edge and compass). (I'm actually using Draftsight which is a free clone of 2d AutoCad.) I figured out that the key internal element is the 36-72-72 triangle (apparently called the Golden Triangle). Once I figured out how to construct a 36-72-72 triangle the pentagon was easy. But I didn't find the key move at all intuitive. I had to cheat and look stuff up. But I learned stuff I didn't know (not much call to construct pentagons in civil engineering). I made a Quicktime movie for you. It's big so I put it on Google Drive. Here's the link: <br />https://drive.google.com/file/d/1jZVa01-aS1ZGuqcfySz5iRkh3qLJOe_6/view?usp=sharingSue VanHattumhttps://www.blogger.com/profile/10237941346154683902noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-7557500827145051992018-09-08T18:40:27.644-07:002018-09-08T18:40:27.644-07:00Thanks for sharing the sciencevsmagic website. It&...Thanks for sharing the sciencevsmagic website. It's a perfect addition to my arsenal for Fun Math Fridays. And it's great fun to play with, regardless of your age!Nataliehttps://www.blogger.com/profile/15849196211716308785noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-87329006589153728742018-09-02T19:36:58.686-07:002018-09-02T19:36:58.686-07:00I got that one this time around. And I finally got...I got that one this time around. And I finally got the pentagon. But I was following directions for that one. Now I'm working on understanding a proof that those directions work. I think it's the only one that needs algebra to understand.Sue VanHattumhttps://www.blogger.com/profile/10237941346154683902noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-63938615309971331922018-08-30T17:05:02.189-07:002018-08-30T17:05:02.189-07:00I bet you gave google your email to make this comm...I bet you gave google your email to make this comment. But I don't get to see it. So I can't email you. But you can email me. mathanthologyeditor at gmail. I'd be happy to give you my syllabus search. Sue VanHattumhttps://www.blogger.com/profile/10237941346154683902noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-16138465977257423722018-08-30T16:37:23.139-07:002018-08-30T16:37:23.139-07:00Can you possibly email me your syllabus search? I ...Can you possibly email me your syllabus search? I can't open it via the link...Brooklyn-Based Math Teacherhttps://www.blogger.com/profile/10741705084695371179noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-50980056356340419292018-03-29T17:37:37.727-07:002018-03-29T17:37:37.727-07:00https://mikesmathpage.wordpress.com/2014/03/09/sue...https://mikesmathpage.wordpress.com/2014/03/09/sue-van-hattums-optimization-problem/<br /><br />This is so cool! You do not need to be teaching calculus to use this activity!Sue VanHattumhttps://www.blogger.com/profile/10237941346154683902noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-76230680163880756552018-01-15T20:43:00.279-08:002018-01-15T20:43:00.279-08:00Thanks for letting me know they fixed it. I am sti...Thanks for letting me know they fixed it. I am still hoping someone will take me up on my alternate version of the puzzle.Sue VanHattumhttps://www.blogger.com/profile/10237941346154683902noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-55113011703255302782018-01-15T20:00:07.190-08:002018-01-15T20:00:07.190-08:00It seems that they have edited the Nautilus post.
...It seems that they have edited the Nautilus post.<br /><br /><em>* This post was edited to clarify that the question is not posed simultaneously, and that both prisoners know who’s asked first.</em>Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-16550595914397762912017-11-16T08:34:53.898-08:002017-11-16T08:34:53.898-08:00Yes my regression does take the data down to 0. Wh...Yes my regression does take the data down to 0. What algebra steps are used to solve this. I know that at whatever time zero the body is 98.6. ...<br />I got it now. ThanksJosephhttps://www.blogger.com/profile/06455349495917896426noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-16586838878542139622017-11-16T07:04:17.264-08:002017-11-16T07:04:17.264-08:00>The data follows an exponential graph but take...>The data follows an exponential graph but takes the data down to 0.<br /><br />It sounds like you mean that your regression takes the graph down to 0. If you want to use regression, instead of doing the algebra, you would need to use excess heat (how high above room temp) as your y values.<br />Sue VanHattumhttps://www.blogger.com/profile/10237941346154683902noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-5834537033327713882017-11-16T06:40:04.722-08:002017-11-16T06:40:04.722-08:00I would figure that the temperature would bottom o...I would figure that the temperature would bottom out at room temperature or 80 degrees on the island. Also, I would figure 98.6 being the temperature just prior to death. The data follows an exponential graph but takes the data down to 0. So when the cup of coffee gets to 2 or 3 hours the temp should be room temp but using the model my regression takes it down to zero. <br />I have tried working some transformations using the equation I find but am at a loss as to how to fix the issue. Josephhttps://www.blogger.com/profile/06455349495917896426noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-11939235642447005922017-10-12T12:25:52.989-07:002017-10-12T12:25:52.989-07:00Someone just complained about readability issues. ...Someone just complained about readability issues. It looks fine from here. Let me know if the formatting is weird.Sue VanHattumhttps://www.blogger.com/profile/10237941346154683902noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-55838453911563143482017-08-31T08:00:14.418-07:002017-08-31T08:00:14.418-07:00Calvin, Email me once to give me your phone number...Calvin, Email me once to give me your phone number, and I am happy to switch to phone.Sue VanHattumhttps://www.blogger.com/profile/10237941346154683902noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-75352180606169122442017-08-30T23:06:32.039-07:002017-08-30T23:06:32.039-07:00Im an old school Gen X/ Millenial cusp. I prefer a...Im an old school Gen X/ Millenial cusp. I prefer a now 'outdated" mode of conversation of communication with people on phones. But I will email soon if you prefer. You just keep living and I hope blessed. P.S. Chlorine is the enemey to the nasal and occular passages, I agree now. From CalvinAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-83504632242620894642017-08-14T21:34:20.641-07:002017-08-14T21:34:20.641-07:00Calvin, please email me! Then we can have a real c...Calvin, please email me! Then we can have a real conversation. You comment actually belongs on my new post. (You'll see.)Sue VanHattumhttps://www.blogger.com/profile/10237941346154683902noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-26386995900342844612017-08-13T23:54:26.474-07:002017-08-13T23:54:26.474-07:00Susan, never forget your inspiration and ability t...Susan, never forget your inspiration and ability to inspire. Sincerely From Calvin in M, MichiganAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-8718914438970930702017-07-10T07:55:14.271-07:002017-07-10T07:55:14.271-07:00None of my students has paid enough attention to n...None of my students has paid enough attention to notice this.I would ask: Do different cups of coffee cool at different rates? What does it depend on?<br /><br />I'm guessing the first person had more insulating body fat (thicker coffee cup), and the second person was smaller overall. <br /><br />But that difference does seem big. I have always just made up the temps, and then found the time and made sure it worked with the clues. Maybe I should keep them closer to one another. I just looked up body cooling (again), and you must tell student this is an oversimplification of real life.<br /><br />I re-read what you wrote, and it's important to say "in the first hour" and never say "per hour". That would indicate a constant rate of change. Every time a student says a thing like that I ask what they think will happen in the second hour, and we return to the graph. Students are so used to straight lines, they want to treat everything the way they do straight lines.<br />Sue VanHattumhttps://www.blogger.com/profile/10237941346154683902noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-82149137409188577492017-07-10T07:11:25.933-07:002017-07-10T07:11:25.933-07:00Hi Sue,
I am working through this project to do w...Hi Sue,<br /><br />I am working through this project to do with my students and have a question that I can't seem to resolve: In the first set of data, the body temperature decreases at a rate of 4.4 degrees in one hour. In the second set of data (assignment 4), the body temperature decreases at a rate of 5.9 degrees in 30 minutes or 11.8 degrees per hour. Since it has a lower starting body temp when found, shouldn't it be decreasing more slowly than the first body found?Denisenoreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-10391527160811076302017-07-04T07:45:00.793-07:002017-07-04T07:45:00.793-07:00Congratulations, Sharon! (I verified her solution....Congratulations, Sharon! (I verified her solution.)<br /><br />The rules for this type of puzzle: use four 4's and no other digits, use any other math symbols you want.Sue VanHattumhttps://www.blogger.com/profile/10237941346154683902noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-72657026563257955452017-07-03T22:28:18.068-07:002017-07-03T22:28:18.068-07:00"A Puzzle: Can you make 109 from four 4's..."A Puzzle: Can you make 109 from four 4's? (I don't promise that it's possible...)"<br /><br />It didn't seem possible... but I found a way to do it. It can be done!Sharon Minsuknoreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-17041354654751703042017-07-01T09:47:55.043-07:002017-07-01T09:47:55.043-07:00So many interesting posts! Good thing I have a lon...So many interesting posts! Good thing I have a long weekend for browsing... Thank you for hosting. :-)Denise Gaskinshttps://www.blogger.com/profile/11928843626113889088noreply@blogger.com