Derek & all:
>It would seem your measure of 32.7273 is probably more accurate and >correct, but this genesis calendar was designed to be a calendar for a >world agricultural and farming culture following the path/cycle of the sun >and its 11 "sunburst" cycles,..... Thanks, Derek! 12-hr clock is imbedded into humans (our minds) that any amount of coaxing is NOT likely to find its way down to common man. However, I showed the possibility to divide the HOUR into any number of parts: so long as this is linked to the HOUR-Angle & hence its further division as the Earth spins in its axis (to detremine local time). Realising this: I changed my stand to revert from 4x100-metric degree (gon) quadrant to the EXISTING 90-degree quadrant; and establish the *decimal linkage - of HOUR and Degree*. I have MY reasons to doubt that it was the 'malafied intentions' of political forces during French Replican Reform for 'time & calendar' that Length Unit - 'Metre, m' was NOT TIED to the base unit for Time - the 'second, s'. It is now TIME to do the rectifying - so advancement in astronomy does NOT suffer! Regards, Brij Bhushan Vij (Tuesday, Kali 5107-W08-02)/265+D-159 (Wednesday, 2006 June 07H14:98(decimal) ET Aa Nau Bhadra Kritvo Yantu Vishwatah -Rg Veda 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" Contact # 001(201)675-8548 >From: "derek winder" <[hidden email]> >To: "Brij Bhushan Vij" <[hidden email]> >Subject: Re: r-sec & 11-Hour Clock Re: Workin' on radian time >Date: Wed, 7 Jun 2006 14:05:41 +0100 > >Brij >I was checking the following which you have wrote and it does appear to fit >the expression 2 (PI) pillars of Hercules/Heracles as shown in genesis >image a combination of secular/linear Metric time measure. > >>If Earth were to remain 2Pi 'radians', the HOUR-angle would be >>32.7273-degree. > >On has always to use 2 digits of measure :- > >the first Cycle measure of 2 digits 32 is dividable by 6 "cycle/days" >the next ratio measure of 2 digits 72 is dividable by 6 giving 12 >ratio/hours. >the next ratio measure of 2 digits 73 is dividable by 5 and 9 producing >14.6 and 8.1111111(cycle~ratio) (2*7"ratio/days" and 2*4"sectors") so in >geo/circle/cycle terms overall it fits 6 ~7 day.. EXACTLY!. > >This would also produce a divided/split 360 degree circle producing a >2*6=12hour, 60min circle of time > >If you multiply the numbers accumulative you get 6*6*7*4=10008 cycles based >on a 5*9=45 degree angle, divide 10008 by 33 angle (solar measure) which >will produce 30.54 54 55 which are 30 days in a month over 3*3 >ratio/cycle yrs of 54 weeks, 54 weeks,and finally a 55 week, which can be >divided again by the solar value11 (2*PI) to produce 5, or in expansion by >the moon 55*.5=27.5 (lunar). > >This 2 (PI) 3*3 cycle/ratio with solar 11 combination produces the >combined "celestial" earth measure image of the sun, moon and earth. >3*3=9*11=99, all it requires therefore is 1 day to be "world day" to fit >100 to 1000+8cycle/hrs/yrs of time. The 8 is the measure of the hour and >the sectors in the circle which are added to 45 degree (1000/8=125/5)=25deg >"shift in time" to produce the genesis "optimum" value (45+25)=70. > >The actual value in degrees therefore in genesis is 32.6 because >54+54+55=163/5=32.6 as in the 6 days of creation (32/6=5.3333333) it just >takes 7 ratio cycle/days (7*3*7)=147/5=24.5hrs to bring it about on a split >12~24 hour basis using the (.5). > >It would seem your measure of 32.7273 is probably more accurate and >correct, but this genesis calendar was designed to be a calendar for a >world agricultural and farming culture following the path/cycle of the sun >and its 11 "sunburst" cycles, simply by using 3 levels forming >symbols/signs geometricaly combined as in the image which would be >understood "visual" as in the created life forms"creatures" and their >"seasons" as one can see in the image, its only when you do the numbers >involved in the cycles that the TIME aspect becomes more understood, but >most people don't want to be bothered with that. > >My instinct and senses now tell me this image is connected with early >India/Egypt and was somehow derived from a projection onto the wall in the >Map room in the great pyramid where it could be observed and recorded on >paper throughout the year by astrologers/astronomers to determine the >moments in the seasons based on the alignment of the sun, moon and the path >of the star Sirius, combined together it forms the "selestial" image of >what one sees as on earth, so one has a sun, moon, star, EARTH chart. > >Derek > > >----- Original Message ----- From: "Brij Bhushan Vij" ><[hidden email]> >To: <[hidden email]> >Sent: Wednesday, May 31, 2006 3:54 PM >Subject: r-sec & 11-Hour Clock Re: Workin' on radian time > > >>Lance, group: >>>>Since it's possible that not everyone has had an >>>opportunity to work on this yet, I won't spoil it by >>>revealing a full set of answers, but I'll release a >>>solution for the original problem. That solution, >>>applied to the 24-hour clock, leads to the general >>>equation to which I referred earlier. >>It is NOT difficult to achieve what Lance has in mind - BUT to what >>advantage? Our minds are set to use 24-hour clock work and 2 Pi radian >>imbedded into our 'conceptions'. For any New adventure, we must be clear >>that any system can be made to work so long as we are 'linking' the *NEW >>TIME UNIT WITH THE NEW LENGTH UNIT* for our clock mechanisms to work for >>astro-calendaric calculations! I show this as: >>Radian Time: 86400/22 sec =3927.273 sec =65.455 min =1hr 5m 27s.273 >>[1s=9,192,631,770 cs-133] >>1. 65.455 min =1hr 5m 27s.273 2. 130.91min =2h 10m 54s.6 >>3. 196.365 min =3h 16m 21s.9 4. 261.82 min =4h 21m 49s.2 >>5. 327.275 min=5h 27m 16s.5 6. 392.73 min =6h 32m 43s.8 >>7. 458.185 min =7h 38m 11s.1 8. 523.64 min =8h 43m 38s.4 >>9. 589.095 min =9h 49m 05s.7 10. 654.55 min =10h 54m 33s >>11. 720.005 min =12-HOURS [Note: the difference of 0.3 sec is due to >>TRUNCATION]. >>The 11-Hour Clock can have HOUR-angle =43200/11 atomic-seconds (or r-sec). >> Thus, r-sec can be defined as: *1/110000th of the atomic day =0.7855 >>s or (72120374745 cs-133~]. If Earth were to remain 2Pi 'radians', the >>HOUR-angle would be 32.7273-degree. >>If a REFORM of 'time & calendar is desired' our thoughts must be practical >>from view point of a man-on-street and that: what this costs to tax-payer? >>Regards, >>Brij Bhushan Vij >>(Tuesday, Kali 5107-W07-02)/265+D-152 (Wednesday, 2006 May >>31H10:88(decimal) ET >>Aa Nau Bhadra Kritvo Yantu Vishwatah -Rg Veda >>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" >>Contact # 001(201)675-8548 >> >> >>>From: Lance Latham <[hidden email]> >>>Reply-To: East Carolina University Calendar discussion List >>><[hidden email]> >>>To: [hidden email] >>>Subject: Re: Workin' on radian time >>>Date: Wed, 31 May 2006 06:37:05 -0700 >>> >>>Group - >>> >>>Since it's possible that not everyone has had an >>>opportunity to work on this yet, I won't spoil it by >>>revealing a full set of answers, but I'll release a >>>solution for the original problem. That solution, >>>applied to the 24-hour clock, leads to the general >>>equation to which I referred earlier. >>> >>>Here goes. >>> >>>The 12-hour clock represents a 12-hour period. There >>>are 2*pi radians in the circle of the clock face, so >>>the hour mark '1' is at an angle: >>> >>> theta = 2*pi = pi >>> ---- ---- radians >>> 12 6 >>> >>>from the position marked '12'. >>> >>>The angular speed of the hour hand, H, is therefore: >>> >>> rH = pi/6 rad/hr >>> >>>Measured in minutes, rH = pi/360 rad/min. >>> >>>The corresponding angle for the minute hand, M, >>>represents 5 minutes, so the angular speed of M is: >>> >>> rM = pi/6 * 1/5 rad = pi/30 rad/min >>> >>>There are several methods for proceeding to a >>>solution. Perhaps the easiest one goes like this. One >>>wishes to solve for the exact time when H and M >>>overlap for the first case, 1:05. Draw a straight line >>>that represents the distance 'd' around the clock >>>face. >>> >>> '12' '1' >>> P0 P1 P2 >>> |--------------|-----------|-------------> d >>> >>>The distances do not have to be to scale. One knows >>>that the distance (P1 - P0) = pi/6 radians. The >>>distance (P2 - P1) can be called 'x'. Initially, set M >>>to P0 and H to P1, to represent the time 1:00. >>> >>>One wishes to advance M at rate rM from P0, and H at >>>rate rH from P1 until M overtakes H at point P2. The >>>difference 'x' represents the time past 1:05 consumed >>>by H while M catches up. >>> >>>A solution for 'x' can be had by setting up 2 >>>equations. Since M and H must both arrive at P2 >>>simultaneously, they spend the same amount of time 't' >>>to do so. Thus one may write: >>> >>> t = x / (pi/360) for H >>> >>>and >>> >>> t = (pi/6 + x) / (pi/30) >>> >>>using the identity: >>> >>> time = distance / rate >>> >>>for both M and H, using their respective distances and >>>rates. >>> >>>One then has the equation of the two, which can be >>>solved for 'x', which turns out to be: >>> >>> x = 5*pi/330 or pi/66 >>> >>>Thus the entire distance (P2 - P0) is: >>> >>> d = pi/6 + x >>> >>>which turns out to be 0.571199 radians. >>> >>>Since 1 radian = 6/pi hours, the conversion from >>>radians to decimal hours is trivial, yielding the >>>result: >>> >>> D = (6/pi) * d = 1.09090909... hours >>> >>>which can then be easily converted to HMS format to >>>yield the final result of: >>> >>> 1:05:27, rounded to the nearest second. >>> >>>This is the exact moment (to the nearest second) when >>>M overtakes H and aligns with it. >>> >>>Some hints for further solution follow below. >>> >>> >>> >>> >>> >>> >>> >>> >>> >>> >>> >>> >>> >>> >>> >>>1. Work the second case for clock time 2:11. From the >>>result, one should be able to deduce a simple formula >>>for calculating the H-M match times for any hour 'h' >>>for a 12-hour clock. (Variable 'h' has values >>>1,2,...11 for a 12-hour clock.) >>> >>>2. Work the first case for a 24-hour clock, i.e., when >>>do H and M align on a 24-hour clock, using the method >>>described, starting with H at '1', M at '12'. >>> >>>3. From the result, one should be able to deduce a >>>simple formula to predict decimal hours, D, from 'h' >>>for an N-hour clock. >>> >>>Good hunting! >>> >>>-Lance >>> >>> >>>Lance Latham >>>[hidden email] >>>Phone: (518) 274-0570 >>>Address: 78 Hudson Avenue/1st Floor, Green Island, NY 12183 >>> >>> >>> >>> >>> >>>__________________________________________________ >>>Do You Yahoo!? >>>Tired of spam? Yahoo! Mail has the best spam protection around >>>http://mail.yahoo.com >> >> >> >> >>-- >>No virus found in this incoming message. >>Checked by AVG Free Edition. >>Version: 7.1.394 / Virus Database: 268.8.0/352 - Release Date: 30/05/2006 >> > |
Derek:
>I get the same result.!! Yes, in the TWO situations you shall get the same result; and I left 'gon' behind since buyers for the Reform of Metrication for Time, were not coming forwards. AND, today I observe infringment or an attempt NOT to grant me the credit for my research - just becuase I am an AUTODIDACT or my affordability to school/college lacked, especially when we had left all our belongings at Lahore (now, Pakistan) as a child of 11-yrs; and wander my childhood in wilderness. The fire in me to be educated kept me going and I STOPPED NOT TO ATTEMPT AND REACH TO TALK OF A POSSIBLE WORLD CALENDAR, fulfilling the needs of tomorrow's society! Yes, I lost my tears when my father died on 14th Januray 1964 who did see my an Engineer. I do not mean to be sentimental. It is only sharing my thought with YOU - why, ask yourself? Regards, Brij Bhushan Vij (Wednesday, Kali 5106-W08-03)/D-160(Thursday, 2006 Jun 08H15:71 (decimal) ET Aa Nau Bhadra Kritvo Yantu Vishwatah -Rg Veda 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" Contact # 001(201)675-8548 >From: "derek winder" <[hidden email]> >To: "Brij Bhushan Vij" <[hidden email]> >Subject: Re: 12_24 hr Sidereal day Re: r-sec & 11-Hour Clock Re: Workin' on >radian time >Date: Thu, 8 Jun 2006 14:21:05 +0100 > >Brij, >Yes i believe your right, i have always known genesis to be accurate it >just depends on the purpose one is using it for, which obviously its not to >measure time to the nearest Time hour angle sec possible, its mainly for >the purpose of measuring/ballancing out the length of the "seasons" over a >period of time using the suns precessional movement and the linnear "line" >metre "hour" and cecular "arc" imperial measure"quadrant". > >Its allbout how you express the measure.! > >If you seperate out the numbers you have produced ( 32.7273 ) you then get >32,72,73 which will form a 3*2digit=6 digit/day level ballancing measure so >combining the "lunar" geo-(27deg) polygon and the "sun" (11deg) quadrant >relative to the star "sirius" (2*.5) timing for counting the earths >rotation.(day~night) > >DOG Calendar. > >SIRIUS/LUNAR "DOGOD" SYSTEM (4,15,( 7 ),15,4)=45 degree arc/angle >SIRIUS/SUN "DOGON" SYSTEM (4,15,( 7 ),15,14)=55 degree arc/angle >(55/11)=5 > >moon 3*9=27 >sun 3*11=33 >sirius 3*2=6 >earth 3*4=12 >total on a 6 day 45deg basis = 27+33+6+12=78/6=13 zodiac signs >total on a 7 day 55deg basis = 27+33+6+12+9(3*3)=87genesis cycles > >3*3*9=81 >3*3*33=297 >3*3*6=54 >3*3*12=108 > >81+297+54+108 total 540cycles /9=90deg/quadrant. > >>Realising this: I changed my stand to revert from 4x100-metric degree >>(gon) >>quadrant to the EXISTING 90-degree quadrant; and establish the *decimal >>linkage - of HOUR and Degree*. > >I get the same result.!! > >Derek > > > >----- Original Message ----- From: "Brij Bhushan Vij" ><[hidden email]> >To: <[hidden email]>; <[hidden email]> >Sent: Wednesday, June 07, 2006 8:00 PM >Subject: 12_24 hr Sidereal day Re: r-sec & 11-Hour Clock Re: Workin' on >radian time > > >>Derek & all: >>>It would seem your measure of 32.7273 is probably more accurate and >>>correct, but this genesis calendar was designed to be a calendar for a >>>world agricultural and farming culture following the path/cycle of the >>>sun >>>and its 11 "sunburst" cycles,..... >>Thanks, Derek! 12-hr clock is imbedded into humans (our minds) that any >>amount of coaxing is NOT likely to find its way down to common man. >>However, I showed the possibility to divide the HOUR into any number of >>parts: so long as this is linked to the HOUR-Angle & hence its further >>division as the Earth spins in its axis (to detremine local time). >>Realising this: I changed my stand to revert from 4x100-metric degree >>(gon) quadrant to the EXISTING 90-degree quadrant; and establish the >>*decimal linkage - of HOUR and Degree*. >>I have MY reasons to doubt that it was the 'malafied intentions' of >>political forces during French Replican Reform for 'time & calendar' that >>Length Unit - 'Metre, m' was NOT TIED to the base unit for Time - the >>'second, s'. It is now TIME to do the rectifying - so advancement in >>astronomy does NOT suffer! >>Regards, >>Brij Bhushan Vij >>(Tuesday, Kali 5107-W08-02)/265+D-159 (Wednesday, 2006 June >>07H14:98(decimal) ET >>Aa Nau Bhadra Kritvo Yantu Vishwatah -Rg Veda >>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" >>Contact # 001(201)675-8548 >> >> >>>From: "derek winder" <[hidden email]> >>>To: "Brij Bhushan Vij" <[hidden email]> >>>Subject: Re: r-sec & 11-Hour Clock Re: Workin' on radian time >>>Date: Wed, 7 Jun 2006 14:05:41 +0100 >>> >>>Brij >>>I was checking the following which you have wrote and it does appear to >>>fit the expression 2 (PI) pillars of Hercules/Heracles as shown in >>>genesis >>>image a combination of secular/linear Metric time measure. >>> >>>>If Earth were to remain 2Pi 'radians', the HOUR-angle would be >>>>32.7273-degree. >>> >>>On has always to use 2 digits of measure :- >>> >>>the first Cycle measure of 2 digits 32 is dividable by 6 "cycle/days" >>>the next ratio measure of 2 digits 72 is dividable by 6 giving 12 >>>ratio/hours. >>>the next ratio measure of 2 digits 73 is dividable by 5 and 9 producing >>>14.6 and 8.1111111(cycle~ratio) (2*7"ratio/days" and 2*4"sectors") so in >>>geo/circle/cycle terms overall it fits 6 ~7 day.. EXACTLY!. >>> >>>This would also produce a divided/split 360 degree circle producing a >>>2*6=12hour, 60min circle of time >>> >>>If you multiply the numbers accumulative you get 6*6*7*4=10008 cycles >>>based on a 5*9=45 degree angle, divide 10008 by 33 angle (solar measure) >>>which will produce 30.54 54 55 which are 30 days in a month over 3*3 >>>ratio/cycle yrs of 54 weeks, 54 weeks,and finally a 55 week, which can be >>>divided again by the solar value11 (2*PI) to produce 5, or in expansion >>>by >>>the moon 55*.5=27.5 (lunar). >>> >>>This 2 (PI) 3*3 cycle/ratio with solar 11 combination produces the >>>combined "celestial" earth measure image of the sun, moon and earth. >>>3*3=9*11=99, all it requires therefore is 1 day to be "world day" to fit >>>100 to 1000+8cycle/hrs/yrs of time. The 8 is the measure of the hour and >>>the sectors in the circle which are added to 45 degree >>>(1000/8=125/5)=25deg "shift in time" to produce the genesis "optimum" >>>value (45+25)=70. >>> >>>The actual value in degrees therefore in genesis is 32.6 because >>>54+54+55=163/5=32.6 as in the 6 days of creation (32/6=5.3333333) it just >>>takes 7 ratio cycle/days (7*3*7)=147/5=24.5hrs to bring it about on a >>>split 12~24 hour basis using the (.5). >>> >>>It would seem your measure of 32.7273 is probably more accurate and >>>correct, but this genesis calendar was designed to be a calendar for a >>>world agricultural and farming culture following the path/cycle of the >>>sun >>>and its 11 "sunburst" cycles, simply by using 3 levels forming >>>symbols/signs geometricaly combined as in the image which would be >>>understood "visual" as in the created life forms"creatures" and their >>>"seasons" as one can see in the image, its only when you do the numbers >>>involved in the cycles that the TIME aspect becomes more understood, but >>>most people don't want to be bothered with that. >>> >>>My instinct and senses now tell me this image is connected with early >>>India/Egypt and was somehow derived from a projection onto the wall in >>>the >>>Map room in the great pyramid where it could be observed and recorded on >>>paper throughout the year by astrologers/astronomers to determine the >>>moments in the seasons based on the alignment of the sun, moon and the >>>path of the star Sirius, combined together it forms the "selestial" image >>>of what one sees as on earth, so one has a sun, moon, star, EARTH chart. >>> >>>Derek >>> >>> >>>----- Original Message ----- From: "Brij Bhushan Vij" >>><[hidden email]> >>>To: <[hidden email]> >>>Sent: Wednesday, May 31, 2006 3:54 PM >>>Subject: r-sec & 11-Hour Clock Re: Workin' on radian time >>> >>> >>>>Lance, group: >>>>>>Since it's possible that not everyone has had an >>>>>opportunity to work on this yet, I won't spoil it by >>>>>revealing a full set of answers, but I'll release a >>>>>solution for the original problem. That solution, >>>>>applied to the 24-hour clock, leads to the general >>>>>equation to which I referred earlier. >>>>It is NOT difficult to achieve what Lance has in mind - BUT to what >>>>advantage? Our minds are set to use 24-hour clock work and 2 Pi radian >>>>imbedded into our 'conceptions'. For any New adventure, we must be clear >>>>that any system can be made to work so long as we are 'linking' the *NEW >>>>TIME UNIT WITH THE NEW LENGTH UNIT* for our clock mechanisms to work for >>>>astro-calendaric calculations! I show this as: >>>>Radian Time: 86400/22 sec =3927.273 sec =65.455 min =1hr 5m 27s.273 >>>>[1s=9,192,631,770 cs-133] >>>>1. 65.455 min =1hr 5m 27s.273 2. 130.91min =2h 10m 54s.6 >>>>3. 196.365 min =3h 16m 21s.9 4. 261.82 min =4h 21m 49s.2 >>>>5. 327.275 min=5h 27m 16s.5 6. 392.73 min =6h 32m 43s.8 >>>>7. 458.185 min =7h 38m 11s.1 8. 523.64 min =8h 43m 38s.4 >>>>9. 589.095 min =9h 49m 05s.7 10. 654.55 min =10h 54m 33s >>>>11. 720.005 min =12-HOURS [Note: the difference of 0.3 sec is due to >>>>TRUNCATION]. >>>>The 11-Hour Clock can have HOUR-angle =43200/11 atomic-seconds (or >>>>r-sec). >>>> Thus, r-sec can be defined as: *1/110000th of the atomic day >>>>=0.7855 s or (72120374745 cs-133~]. If Earth were to remain 2Pi >>>>'radians', the HOUR-angle would be 32.7273-degree. >>>>If a REFORM of 'time & calendar is desired' our thoughts must be >>>>practical from view point of a man-on-street and that: what this costs >>>>to >>>>tax-payer? >>>>Regards, >>>>Brij Bhushan Vij >>>>(Tuesday, Kali 5107-W07-02)/265+D-152 (Wednesday, 2006 May >>>>31H10:88(decimal) ET >>>>Aa Nau Bhadra Kritvo Yantu Vishwatah -Rg Veda >>>>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" >>>>Contact # 001(201)675-8548 >>>> >>>> >>>>>From: Lance Latham <[hidden email]> >>>>>Reply-To: East Carolina University Calendar discussion List >>>>><[hidden email]> >>>>>To: [hidden email] >>>>>Subject: Re: Workin' on radian time >>>>>Date: Wed, 31 May 2006 06:37:05 -0700 >>>>> >>>>>Group - >>>>> >>>>>Since it's possible that not everyone has had an >>>>>opportunity to work on this yet, I won't spoil it by >>>>>revealing a full set of answers, but I'll release a >>>>>solution for the original problem. That solution, >>>>>applied to the 24-hour clock, leads to the general >>>>>equation to which I referred earlier. >>>>> >>>>>Here goes. >>>>> >>>>>The 12-hour clock represents a 12-hour period. There >>>>>are 2*pi radians in the circle of the clock face, so >>>>>the hour mark '1' is at an angle: >>>>> >>>>> theta = 2*pi = pi >>>>> ---- ---- radians >>>>> 12 6 >>>>> >>>>>from the position marked '12'. >>>>> >>>>>The angular speed of the hour hand, H, is therefore: >>>>> >>>>> rH = pi/6 rad/hr >>>>> >>>>>Measured in minutes, rH = pi/360 rad/min. >>>>> >>>>>The corresponding angle for the minute hand, M, >>>>>represents 5 minutes, so the angular speed of M is: >>>>> >>>>> rM = pi/6 * 1/5 rad = pi/30 rad/min >>>>> >>>>>There are several methods for proceeding to a >>>>>solution. Perhaps the easiest one goes like this. One >>>>>wishes to solve for the exact time when H and M >>>>>overlap for the first case, 1:05. Draw a straight line >>>>>that represents the distance 'd' around the clock >>>>>face. >>>>> >>>>> '12' '1' >>>>> P0 P1 P2 >>>>> |--------------|-----------|-------------> d >>>>> >>>>>The distances do not have to be to scale. One knows >>>>>that the distance (P1 - P0) = pi/6 radians. The >>>>>distance (P2 - P1) can be called 'x'. Initially, set M >>>>>to P0 and H to P1, to represent the time 1:00. >>>>> >>>>>One wishes to advance M at rate rM from P0, and H at >>>>>rate rH from P1 until M overtakes H at point P2. The >>>>>difference 'x' represents the time past 1:05 consumed >>>>>by H while M catches up. >>>>> >>>>>A solution for 'x' can be had by setting up 2 >>>>>equations. Since M and H must both arrive at P2 >>>>>simultaneously, they spend the same amount of time 't' >>>>>to do so. Thus one may write: >>>>> >>>>> t = x / (pi/360) for H >>>>> >>>>>and >>>>> >>>>> t = (pi/6 + x) / (pi/30) >>>>> >>>>>using the identity: >>>>> >>>>> time = distance / rate >>>>> >>>>>for both M and H, using their respective distances and >>>>>rates. >>>>> >>>>>One then has the equation of the two, which can be >>>>>solved for 'x', which turns out to be: >>>>> >>>>> x = 5*pi/330 or pi/66 >>>>> >>>>>Thus the entire distance (P2 - P0) is: >>>>> >>>>> d = pi/6 + x >>>>> >>>>>which turns out to be 0.571199 radians. >>>>> >>>>>Since 1 radian = 6/pi hours, the conversion from >>>>>radians to decimal hours is trivial, yielding the >>>>>result: >>>>> >>>>> D = (6/pi) * d = 1.09090909... hours >>>>> >>>>>which can then be easily converted to HMS format to >>>>>yield the final result of: >>>>> >>>>> 1:05:27, rounded to the nearest second. >>>>> >>>>>This is the exact moment (to the nearest second) when >>>>>M overtakes H and aligns with it. >>>>> >>>>>Some hints for further solution follow below. >>>>> >>>>> >>>>> >>>>> >>>>> >>>>> >>>>> >>>>> >>>>> >>>>> >>>>> >>>>> >>>>> >>>>> >>>>> >>>>>1. Work the second case for clock time 2:11. From the >>>>>result, one should be able to deduce a simple formula >>>>>for calculating the H-M match times for any hour 'h' >>>>>for a 12-hour clock. (Variable 'h' has values >>>>>1,2,...11 for a 12-hour clock.) >>>>> >>>>>2. Work the first case for a 24-hour clock, i.e., when >>>>>do H and M align on a 24-hour clock, using the method >>>>>described, starting with H at '1', M at '12'. >>>>> >>>>>3. From the result, one should be able to deduce a >>>>>simple formula to predict decimal hours, D, from 'h' >>>>>for an N-hour clock. >>>>> >>>>>Good hunting! >>>>> >>>>>-Lance >>>>> >>>>> >>>>>Lance Latham >>>>>[hidden email] >>>>>Phone: (518) 274-0570 >>>>>Address: 78 Hudson Avenue/1st Floor, Green Island, NY 12183 >>>>> >>>>> >>>>> >>>>> >>>>> >>>>>__________________________________________________ >>>>>Do You Yahoo!? >>>>>Tired of spam? Yahoo! Mail has the best spam protection around >>>>>http://mail.yahoo.com >>>> >>>> >>>> >>>> >>>>-- >>>>No virus found in this incoming message. >>>>Checked by AVG Free Edition. >>>>Version: 7.1.394 / Virus Database: 268.8.0/352 - Release Date: >>>>30/05/2006 >>>> >>> >> >> >> >> >>-- >>No virus found in this incoming message. >>Checked by AVG Free Edition. >>Version: 7.1.394 / Virus Database: 268.8.2/357 - Release Date: 06/06/2006 >> >> > |
Free forum by Nabble | Edit this page |