tag:blogger.com,1999:blog-2433841880619171855.post2961929524672135690..comments2024-03-27T21:09:44.320+00:00Comments on Pat'sBlog: Harmony, and Harmonic ProblemsUnknownnoreply@blogger.comBlogger4125tag:blogger.com,1999:blog-2433841880619171855.post-71571957218660253062012-10-18T22:19:03.210+01:002012-10-18T22:19:03.210+01:00Dennis, and others, it is half the harmonic mean (...Dennis, and others, it is half the harmonic mean (since we combine two things working at the "average" speed.Pat's Bloghttps://www.blogger.com/profile/15234744401613958081noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-20022482608566033712009-01-30T19:22:00.000+00:002009-01-30T19:22:00.000+00:00Pat: In your cistern example, how can the answer b...Pat: In your cistern example, how can the answer be three and three-quarters? That's more time than the first pipe requires alone. Wouldn't the answer be half of the harmonic mean?<BR/><BR/>Then in the problem of the inscribed square in a right triangle, isn't the length of each side of the square half the harmonic mean?<BR/><BR/>DennisAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-82010169207733037832008-11-23T16:39:00.000+00:002008-11-23T16:39:00.000+00:00Thanks Dave; and I should add that I failed to men...Thanks Dave; and I should add that I failed to mention many variations of the problem that problem solvers may encounter across history. In the 1400's, Smith mentions, the animals eating a goat version (if a lion can eat a goat in three days and a tiger in five days...). Later, in the mid 1500's, problems involving A building a house in five days and B building a house in ten days, appeared. Today it is most often seen, it seems, in questions about driving from here to there and back at different speeds. In each case, the result leads to the Harmonic mean.Pat's Bloghttps://www.blogger.com/profile/15234744401613958081noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-6658227767549701342008-11-23T04:03:00.000+00:002008-11-23T04:03:00.000+00:00Pat, we share a passion for the history of mathema...Pat, we share a passion for the history of mathematics and how seemingly unrelated ideas are interconnected. I didn't expect the harmonic mean to appear in my square in the triangle problem. Yet somehow I wasn't that surprised when it did!<BR/><BR/>Thanks for the reference and I enjoyed reading your post. BTW, I haven't participated or even looked at math-learn, math-teach or those other forums to which I used to post, but it was nice to find your blog and see your name again after all these years...<BR/>Dave MarainDave Marainhttps://www.blogger.com/profile/13321770881353644307noreply@blogger.com