tag:blogger.com,1999:blog-5303307482158922565.post5412914639692790545..comments2024-03-22T13:39:55.941-07:00Comments on Math Mama Writes...: Calculus: e and pi Are Both TranscendentalSue VanHattumhttp://www.blogger.com/profile/10237941346154683902noreply@blogger.comBlogger3125tag:blogger.com,1999:blog-5303307482158922565.post-48354817812200237262014-03-17T17:03:11.119-07:002014-03-17T17:03:11.119-07:00Hi Sue,
you should check out Michael Spivak's...Hi Sue,<br /><br />you should check out Michael Spivak's Calculus. The entire 16th chapter is devoted to proving the irrationality of Pi. He's very thorough and doesn't skip "obvious" steps like Niven's classic half-page proof linked above (although Niven's proof is not aimed at the same audience, e.g. professional mathematicians). Spivak's (treatment of the) proof was the first proof that I was able to grasp.<br /><br />Also, you should also see this (other classic) integral @ http://www.thedudeminds.net/?p=4768 (it's in french but you'll get the math parts for sure) which links nicely 22/7 and Pi.<br /><br />Cheers !The Dudehttps://www.blogger.com/profile/09582233217452159286noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-85718168160264934562014-03-14T14:41:03.321-07:002014-03-14T14:41:03.321-07:00http://projecteuclid.org/download/pdf_1/euclid.bam...http://projecteuclid.org/download/pdf_1/euclid.bams/1183510788timteachesmathhttps://www.blogger.com/profile/09721346163506388968noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-33836247640899132122014-03-14T14:29:49.669-07:002014-03-14T14:29:49.669-07:00I'm honored to find out I am one of your favor...I'm honored to find out I am one of your favorite bloggers! =) You can find the proof that pi is irrational here: http://mathlesstraveled.com/post-series/ Scroll down to "Irrationality of Pi". The proof that e is irrational is actually much simpler than the proof for pi --- I hope to write about it at some point, once I get back to blogging regularly again (at the moment I'm trying to finish my PhD dissertation). It seems there are proofs of the transcendence of e and pi which are about the same level of difficulty as the proof of pi's irrationality, but I haven't looked carefully at them myself.Brenthttps://www.blogger.com/profile/14440861005012132386noreply@blogger.com