tag:blogger.com,1999:blog-5303307482158922565.post5576846723983735194..comments2017-03-18T21:09:07.956-07:00Comments on Math Mama Writes...: The Roots of Calculus - ArchimedesSue VanHattumhttp://www.blogger.com/profile/10237941346154683902noreply@blogger.comBlogger9125tag:blogger.com,1999:blog-5303307482158922565.post-57392998656175474532016-01-20T01:04:17.167-08:002016-01-20T01:04:17.167-08:00I showed the quadrature of the parabola to my math...I showed the quadrature of the parabola to my math history students last year. It's astounding! (It's also pretty difficult, and you'll probably want to be able to have time to "follow along" on your own paper.) I liked this website, which has step by step diagrams to go with the text. http://web.calstatela.edu/faculty/hmendel/Ancient%20Mathematics/Archimedes/QuadraturaParabolae/QP.contents.htmlEvelynhttp://www.blogger.com/profile/08903667625039887922noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-1259324803634480912016-01-02T17:09:56.107-08:002016-01-02T17:09:56.107-08:00The circumscribed looks lots harder to figure out....The circumscribed looks lots harder to figure out. I'm not seeing the pattern yet.Sue VanHattumhttp://www.blogger.com/profile/10237941346154683902noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-37537633673126230092016-01-02T10:14:44.712-08:002016-01-02T10:14:44.712-08:00Yes. And your comment got me back to playing in ge...Yes. And your comment got me back to playing in geogebra and on paper, to try to figure this all out. I'm now working on a handout for my students.Sue VanHattumhttp://www.blogger.com/profile/10237941346154683902noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-35759898443538618282016-01-02T09:18:52.259-08:002016-01-02T09:18:52.259-08:00Archimedes also used a circumscribed hexagon as we...Archimedes also used a circumscribed hexagon as well, so he established not just a lower bound, but an upper bound.Buddha Buckhttp://www.blogger.com/profile/17167036913705912859noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-62334976053290530172015-12-28T19:36:54.040-08:002015-12-28T19:36:54.040-08:00Yes. I don't know what hiccup in my attention ...Yes. I don't know what hiccup in my attention made me chop that up like that. I will fix it.Sue VanHattumhttp://www.blogger.com/profile/10237941346154683902noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-44863764815782501262015-12-28T10:39:24.512-08:002015-12-28T10:39:24.512-08:00Don't you mean the lower bound on pi is 3=6/2?...Don't you mean the lower bound on pi is 3=6/2?Win Smithhttp://www.blogger.com/profile/03925765417737217106noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-38335891588708178202015-12-25T02:38:00.354-08:002015-12-25T02:38:00.354-08:00I'm not sure this counts as starting with Arch...I'm not sure this counts as starting with Archimedes, but your post made me wonder if he was credited with responses to any of Zeno's paradoxes. Wikipedia says yes: <a href="https://en.wikipedia.org/wiki/Zeno%27s_paradoxes#Proposed_solutions" rel="nofollow">Proposed Solutions</a> with the sum of an infinite geometric series.<br /><br />Also, there's always this song from Square 1 TV to enjoy: <a href="https://www.youtube.com/watch?v=Bz6VtQJ6-kA" rel="nofollow">Archimedes Song</a>Joshua Greenehttp://www.blogger.com/profile/11702319994021721608noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-52244382206996483792015-12-24T15:56:11.221-08:002015-12-24T15:56:11.221-08:00The cool thing is how easy to see why this is pi.The cool thing is how easy to see why this is pi.Sue VanHattumhttp://www.blogger.com/profile/10237941346154683902noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-49513563171672746292015-12-24T14:44:55.584-08:002015-12-24T14:44:55.584-08:00I showed this method to Math Circle for Pi day a l...I showed this method to Math Circle for Pi day a long time ago. We discovered that it converges very very slowly. (but I think it's still a bit faster than the arctan taylor series.)Haohttp://www.blogger.com/profile/02348974241652264510noreply@blogger.com