JM Steele, sir: >.....That creates a class of approximants with the same property, but varying >numbers of digits. I thank you for this. I have no dispute with 'mathematicians'. My only point had/has been the the *application of Pi* could be simplified with yet another approximation which fulfill the general use of Radian and the Value for Pi, as you rightly put: 180/Pi as arc-angle of ONE degree - I use in arriving at the Nautical Kilometre as 1/100th of this. It is like saying: -1, 0, 1,2 3,Pi,4,5..... a point on number line. The application of Radian =57*17'44".88 and Pi =100000/31831 satisfy the EQUATION: A circle has 2 Pi Radians, or else there has to be a "constancy factor" as : CIRCLE = 2 k Pi r, to place the sign of equality! Regards, Brij Bhushan Vij Monday (Memorial Day) 20110530H20:23(decimal)EST Aa Nau Bhadra Kritvo Yantu Vishwatah -Rg Veda The Astronomical Poem (revised number of days in any month) "30 days has July,September, April, June, November and December all the rest have 31 except February which has 29 except on years divisible evenly by 4; except when YEAR divisible by 128 and 3200 - as long as you remember that "October (meaning 8) is the 10th month; and December (meaning 10) is the 12th BUT has 30 days & ONE OUTSIDE of calendar-format" Jan:31; Feb:29; Mar:31; Apr:30; May:31; Jun:30 Jul:30; Aug:31; Sep:30; Oct:31; Nov:30; Dec:30 (365th day of Year is World Day) ******As per Kali V-GRhymeCalendaar***** "Koi bhi cheshtha vayarth nahin hoti, purshaarth karne mein hai" My Profile - http://www.brijvij.com/bbv_2col-vipBrief.pdf Author had NO interaction with The World Calendar Association except via Media & Organisations to who I contributed for A Possible World Calendar, since 1971. HOME PAGE: http://www.brijvij.com/ Contact via E-mail: [email protected]
Date: Mon, 30 May 2011 12:25:48 -0700 From: [email protected] Subject: [USMA:50538] Re: Pi closer to ABSOLUTE RE: Re: Value of pi To: [email protected] Brij 0.31831 is just the five digit approximation to 1/pi. It may also be written as 31831/100000. Obviously the reciprocal approximates pi. Since the degrees per radian constant is 180/pi, any approximant to 1/pi with a finite number of decimals results in the radian constant having a finite number of decimals (one less actually). If that is an important property in your application, you can simply take more digits to the 1/pi approximation, write it as a common fraction and invert it. That creates a class of approximants with the same property, but varyin numbers of digits. From: Brij Bhushan Vij <[email protected]> To: U.S. Metric Association <[email protected]> Sent: Mon, May 30, 2011 12:45:53 AM Subject: [USMA:50537] Pi closer to ABSOLUTE RE: Re: Value of pi JM Steele, Pat Naughtin & all Sirs: In my note/reply to Victor on May 11, I wrote: "Pi RE: Growth, Aging & Decay RE: Time" To see messages related to this one, group messages by conversation. 5/11/11 Brij Bhushan Vij Brij Bhushan Vij [email protected] To calendar listserv From: Brij Bhushan Vij ([email protected]) Sent: Wed 5/11/11 4:13 PM To: calendar listserv ([email protected]) Victor, Sepp sirs: >.....very true! NO wonder. Measure of Geometry via Arc-angle [and Pi] is related to TIME. Pi is a point on NUMBER LINE that lies between 3.1415...and 3.1416; which can be equated to 100000/31831, which repeats all by itself at 5244th decimal point. I was checking on THIS aspect of *yet another value for Pi* that fits almost every aspect: Pi value = 104348/33215 gives Radian =57* 17’ 44”.8062253229577951 Brij's (Rationalised)Pi =100000/31831 give Radian =57* 17’ 44”.880000000000000000000000009657 206264.88 Arc-seconds = 57* 17’ 44”.88 Approximation of 'Chord-length' of the circle to 'length of circumference' has so far defied mathematicians/calendar makers alike. Recently, March 14th was declared as Pi-day, which is 74th day after (January 01):http://www.brijvij.com/bb_fbUNday-we! ek.pdf Regards, Brij Bhushan Vij Wednesday , 20110511H16:18(decimal)EST" >.....Pi value 355/113 or 104348/33215 and the earlier 22/7 or underroot 10.... As in my previous arguments and elucidations, I expressed my Pi value to be closer to ABSOLUTE and repeating ALL by itself at 5244th decimal point, I work to show *how close to actual is my RESULT* when compared to these above values: >http://en.wikipedia.org/wiki/Pi & http://en.wikipedia.org/wiki/Indiana_Pi_Bill >http://en.wikipedia.org/wiki/Piphilology It is interesting, learning: The Indiana Pi Bill is the popular name for bill #246 of the 1897 sitting of the Indiana General Assembly, one of the most famous attempts to establish scientific truth by legislative fiat. 22/7 =3.1428571428571428571428571428571 give RADIAN =57*.27272727272727272727272727273 i.e. 57* 16’ 21”.818181818181818181818181827554 SqrRoot 10 =3.1622776601683793319988935444327 give RADIAN =56*.920997883030827975980083799802 i.e. 56* 55’ 15”.592378910980713528301679286722 355/113 =3.1415929203539823008849557522124 give RADIAN =57*.295774647887323943661971830986 i.e. 57* 17’ 44”.788732394366197183098591549296 104348/33215 =3.1415926539214210447087159415927 give RADIAN = 57*.295779507034154943075094874854=57*17’44”.806225322957795070341549473685 Against these values, my result seem to be the BEST100000/31831 =3.141591530269234394144073387 5781 is possibly *SIMPLEST, BEST & EASY to memorise* which give RADIAN =57* 17’ 44”.880000000000000000000000009657 i.e. 57*.2958 for ALL calculations! On my examining the value during 1973-74, I had the value run into Delhi University Campus, Computer Center and published its value to lie between TWO FRACTIONS, and later got this copyrighted as the “POSSIBLE ABSOLUTE VALUE”. Let this be the YET ANOTHER VALUE till I am proved WRONG in my argument advanced during discussions with USMA & Calndr-L members on list (see archives’). Mathematicians may in due course see reason in my pointing to THIS value being *absolute & unique*. My regards, sirs Brij Bhushan Vij Monday (Memorial Day), 20110530H00:74(decimal)EST Aa Nau Bhadra Kritvo Yantu Vishwatah -Rg Veda The Astronomical Poem (revised number of days in any month) "30 days has July,September, April, June, November and December all the rest have 31 except February which has 29 except on years divisible evenly by 4; except when YEAR divisible by 128 and 3200 - as long as you remember that "October (meaning 8) is the 10th month; and December (meaning 10) is the 12th BUT has 30 days & ONE OUTSIDE of calendar-format" Jan:31; Feb:29; Mar:31; Apr:30; May:31; Jun:30 Jul:30; Aug:31; Sep:30; Oct:31; Nov:30; Dec:30 (365th day of Year is World Day) ******As per Kali V-GRhymeCalendaar***** "Koi bhi cheshtha vayarth nahin hoti, purshaarth karne mein hai" My Profile - http://www.brijvij.com/bbv_2col-vipBrief.pdf Author had NO interaction with The World Calendar Association except via Media & Org! anisations to who I contributed for A Possible World Calendar, since 1971. HOME PAGE: http://www.brijvij.com/ Contact via E-mail: [email protected] Date: Sun, 29 May 2011 10:12:51 -0700 From: [email protected] Subject: [USMA:50536] Re: Value of pi To: [email protected] Weren't we all. Most scientific calculators have a "pi" key, but if you are forced to use a simple calculator, 355/113 is a good enough approximation for virtually any engineering work (better than 0.1 ppm). Write it as a classic long division problem and you will never forget it. Much less mnemonic, but 104348/33215 agrees with the pi key on my 10 digit calculator. If I subtract them, the calculator gives zero. From: Pat Naughtin <[email protected]> To: U.S. Metric Association <[email protected]> Sent: Sun, May 29, 2011 6:45:54 AM Subject: [USMA:50533] Value of pi On a more serious note, I was brought up in my early education to believe that pi was equal to 22/7 and that all circles had a radius that was a multiple or sub-multiple of 7. These days, if I want a quick value for a circular area I use diameter squared multiplied by 0.8, where 0.8 is an approximation of pi/4 (pi/4 = 0.7854). As an example, my garden rainwater tank is 3 metres in diameter and it is 2 metres up to the overflow pipe. My estimate of its volume, done in my head, goes something like this: 3 metres squared = 9 square metres. 9 square metres times 0.8 = 7.2 square metres = area of the base of the tank (say) 7 square metres. 7 square metres times 2 = 14 cubic metres or 14 000 litres. When I bought this tank it was specified to hold 13 500 litres so it looks like I got a good deal. Cheers, Pat Naughtin Geelong Australia
