From mboxrd@z Thu Jan 1 00:00:00 1970 X-Spam-Checker-Version: SpamAssassin 3.4.4 (2020-01-24) on polar.synack.me X-Spam-Level: X-Spam-Status: No, score=-1.9 required=5.0 tests=BAYES_00 autolearn=ham autolearn_force=no version=3.4.4 X-Google-Language: ENGLISH,ASCII-7-bit X-Google-Thread: 103376,cc4f25d878383cc X-Google-Attributes: gid103376,public X-Google-ArrivalTime: 2001-12-11 14:45:20 PST Path: archiver1.google.com!news1.google.com!sn-xit-02!supernews.com!newsfeed.direct.ca!look.ca!howland.erols.net!news-out.worldnet.att.net.MISMATCH!wn3feed!wn2feed!worldnet.att.net!204.127.198.204!attbi_feed4!attbi.com!rwcrnsc53.POSTED!not-for-mail From: "Mark Lundquist" Newsgroups: comp.lang.ada References: <11bf7180.0112070815.2625851b@posting.google.com> <9v0crt$bo2bi$1@ID-25716.news.dfncis.de> <9v37rs$cdmva$1@ID-25716.news.dfncis.de> Subject: Re: Dimensionality Checking (Ada 20XX) X-Priority: 3 X-MSMail-Priority: Normal X-Newsreader: Microsoft Outlook Express 5.50.4133.2400 X-MimeOLE: Produced By Microsoft MimeOLE V5.50.4133.2400 Message-ID: <30wR7.37507$Yy.396223@rwcrnsc53> NNTP-Posting-Host: Q_vR7-215610-Yy-395784@rwcrnsc53 X-Complaints-To: abuse@attbi.com X-Trace: rwcrnsc53 1008110719 Q_vR7-215610-Yy-395784@rwcrnsc53 (Tue, 11 Dec 2001 22:45:19 GMT) NNTP-Posting-Date: Tue, 11 Dec 2001 22:45:19 GMT Organization: AT&T Broadband Date: Tue, 11 Dec 2001 22:45:20 GMT Xref: archiver1.google.com comp.lang.ada:17789 Date: 2001-12-11T22:45:20+00:00 List-Id: "Stephen Leake" wrote in message news:upu5ln22l.fsf@gsfc.nasa.gov... > > It is simply wrong to try to define units for trig and exponential > functions. Remember the Taylor expansion for Sin: > > Sin (x) = x - 1/6 x**3 ... > > If x has dimensions of meters (shudder :), then what are the > dimensions of Sin (x)? Hokey smokes, it's the ratio of two sides of a triangle, so its dimensions are Distance/Distance! Forget the Taylor series! > This is why angles must be dimensionless, as > radians are. Angles are not dimensionless. They are the ratio of distance around the circumference to the radius. That's why for radian, there's 2 * Pi of 'em in a circle. The SI defines the units of radians as (m * m**-1) ('m' stands for 'meters'). I don't get why people keep saying radians are dimensionless. Cheers, Mark