tag:blogger.com,1999:blog-2433841880619171855.comments2024-11-02T15:09:19.707+00:00Pat'sBlogUnknownnoreply@blogger.comBlogger1289125tag:blogger.com,1999:blog-2433841880619171855.post-63637584122832039882024-10-20T22:31:51.844+01:002024-10-20T22:31:51.844+01:00Patrick, Thank you for your continued support. I ...Patrick, Thank you for your continued support. I assure you, come January first I will be realigned with the correct day date for another three years. I hope if I'm still around by March 1st 2028, you will still be around to correct my errors for another ten months.<br /><br />Pat BPat's Bloghttps://www.blogger.com/profile/15234744401613958081noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-2406826147230679552024-10-15T21:24:55.847+01:002024-10-15T21:24:55.847+01:00so cool!so cool!John Goldenhttps://www.blogger.com/profile/18212162438307044259noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-30352312140028800672024-10-15T17:36:13.505+01:002024-10-15T17:36:13.505+01:00John, Almost, but not Arabic. The term was used f...John, Almost, but not Arabic. The term was used for Aryabhatta, a fifth century Indian scholar in his Sanskrit verse. And he apparently was one of the first to use the half chord. Ptolemy and other Greeks used the full chord length (2 x Sine) and because much Indian and Arabic work was ignored, early Western work followed a similar approach. He didn't actually give the half-chord, "jya" directly but in a set of first differences for each increment of 3 3/4 degrees. They also were not ratios but half chords of a circle of fixed radius. His radius was 3438, derived from the product of his four digit pin and the number of arc minutes in a 360 degree circle, 21,600. His first distance I have recorded as 225; the halve chord of a 3 3/4 degree arc, which I think was pretty close. <br />Thanks for the additional input.<br /><br />Hope you are well,<br /><br />Pat BPat's Bloghttps://www.blogger.com/profile/15234744401613958081noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-72386103201579557332024-10-15T14:55:37.119+01:002024-10-15T14:55:37.119+01:00I'd heard that the original arabic term was fo...I'd heard that the original arabic term was for 'bowstring' which is very visually significant for the look of sine in the unit circle, especially if it's now half of what it originally was.John Goldenhttps://www.blogger.com/profile/18212162438307044259noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-23067319579242571012024-10-11T00:46:34.828+01:002024-10-11T00:46:34.828+01:00You've never seen anything like it.You've never seen anything like it.jackvh2001@gmail.comhttps://www.blogger.com/profile/07149477008235423625noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-50074841281316656452024-09-06T13:45:11.401+01:002024-09-06T13:45:11.401+01:00Good morning. Today is the 250th day of the year....Good morning. Today is the 250th day of the year. Hope you are well.Patrickhttps://www.blogger.com/profile/12361329093650973354noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-28556290990895298772024-08-21T16:50:21.503+01:002024-08-21T16:50:21.503+01:00Good morning! Today is the 234th day of the year,...Good morning! Today is the 234th day of the year, not 233rd.Patrickhttps://www.blogger.com/profile/12361329093650973354noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-9010769055383872542024-07-28T18:42:48.964+01:002024-07-28T18:42:48.964+01:00Thank you, Glad you found it interesting.
Pat BThank you, Glad you found it interesting.<br /><br />Pat BPat's Bloghttps://www.blogger.com/profile/15234744401613958081noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-28103019543247944862024-07-13T20:30:40.951+01:002024-07-13T20:30:40.951+01:00What help do you need !! Just ask for it. What help do you need !! Just ask for it. HelperEnergyhttps://www.blogger.com/profile/03978259865417874672noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-4254753055583641712024-07-13T15:52:35.577+01:002024-07-13T15:52:35.577+01:00Always okay to include me! A genuine honor. A coup...Always okay to include me! A genuine honor. A couple of the results are here https://mathhombre.tumblr.com/post/752639784111964160/odd-magic-squaresJohn Goldenhttps://www.blogger.com/profile/18212162438307044259noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-22302348670028999282024-07-13T14:38:49.200+01:002024-07-13T14:38:49.200+01:00John, very interesting. I remember trying to play...John, very interesting. I remember trying to play around with magic sauares and sequences, but it was before I learned of the diagonals to square method. If you do more, let me know what you find. And is it OK if I include your observations in future versions of this topic? <br />Be well, my friend.<br /><br />PatPat's Bloghttps://www.blogger.com/profile/15234744401613958081noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-7453464302627175192024-07-11T16:18:55.037+01:002024-07-11T16:18:55.037+01:00A fantastic article - well written!A fantastic article - well written!Simonhttps://www.blogger.com/profile/11925183170598299953noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-26985909432426181962024-06-07T01:09:51.294+01:002024-06-07T01:09:51.294+01:00Love this! Was playing around and you can use any ...Love this! Was playing around and you can use any linear sequence for the 5 diagonal rows, and the rows and columns are still magic. And one diagonal? Have to think about it some more.<br /><br />https://docs.google.com/spreadsheets/d/1hWLRhtwfqT2X-9H2iFatkz6E1mOJMnC8ToGRyFaoqM8/edit?usp=sharing John Goldenhttps://www.blogger.com/profile/18212162438307044259noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-47378563865297311322024-06-03T14:01:03.354+01:002024-06-03T14:01:03.354+01:00I found your discussion on Rheticus and the evolut...I found your discussion on Rheticus and the evolution of trigonometric terminology incredibly insightful. As a <a href="https://smiletutor.sg/maths-tuition/" rel="nofollow">math tutor</a>, it's fascinating to see the historical contexts that shaped the concepts I teach today. This deeper understanding will definitely enrich how I present these ideas to my students!Johnhttps://www.blogger.com/profile/14159093826413038804noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-892139184415438452024-05-30T20:29:32.889+01:002024-05-30T20:29:32.889+01:00Hey. Today is day 151! Figured I would periodica...Hey. Today is day 151! Figured I would periodically give you a heads up about having the wrong day of the year. Take care!Patrickhttps://www.blogger.com/profile/12361329093650973354noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-5140965676509636812024-05-28T19:12:42.157+01:002024-05-28T19:12:42.157+01:00Click here to get ðŸ‘‰Distance CalculatorClick here to get ðŸ‘‰<a href="https://gbreducation.blogspot.com/2024/05/distance-calculator.html?m=1" rel="nofollow">Distance Calculator</a>Kamlesh Yadavhttps://www.blogger.com/profile/14505002513495061590noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-83434825174785679192024-05-28T10:56:37.582+01:002024-05-28T10:56:37.582+01:00The issue isn't with the obelus, but with not ...The issue isn't with the obelus, but with not correctly parsing Terms. Terms are separated by operators and joined by grouping symbols. So in the example iÃ·rt vs. iÃ·rxt, in the former rt is a single term entirely in the denominator, whereas in the latter r and t have been split into 2 separate terms, which has the effect of taking the t out of the denominator and flipping it into the numerator. Since rt is a single Term, the only way you can add a multiplication sign to it is if you also put it in brackets, to keep it as 1 term. i.e. iÃ·(rxt).<br /><br />And yes, more than 100 years ago it was the case that everything following the obelus was in the denominator, but that changed, not sure when, but certainly by Lennes' time (1917) such that only the first term following the obelus was in the denominator, such that you could then have multiple divisions within the same line (instead of only one, which was the limitation with the previous usage) - this is the same usage we have today.<br /><br />I have a whole thread about the common order of operations mistakes at https://dotnet.social/@SmartmanApps/110897908266416158Smartman Appshttps://www.blogger.com/profile/05654402875586198882noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-31838558313884448502024-05-23T20:19:51.432+01:002024-05-23T20:19:51.432+01:00Good afternoon! It is the 144th day of the year -...Good afternoon! It is the 144th day of the year - you have had the wrong day of the year for a little while. Good luck!Patrickhttps://www.blogger.com/profile/12361329093650973354noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-85120274398551231162024-05-16T21:14:51.158+01:002024-05-16T21:14:51.158+01:00Thank you for this! I'm doing some research in...Thank you for this! I'm doing some research in this area and you've taught me a few things I wasn't aware of. I may also look into Dr Loweke's book. I got my master's from Wayne state! Is this still an active blog?TutorMyMath.comhttps://www.blogger.com/profile/14112017509226704457noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-64726852051969417322024-05-10T13:03:31.707+01:002024-05-10T13:03:31.707+01:00Good morning. With the leap year, today is day 13...Good morning. With the leap year, today is day 131. Figured you want to correct this at some point this year. Thanks for all your hard work on the blog.Patrickhttps://www.blogger.com/profile/12361329093650973354noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-1866872925579968412024-05-07T20:27:48.834+01:002024-05-07T20:27:48.834+01:00MAY SEVENTH or May 7th or 5-7 or 5/7
5 and 7 Bli...MAY SEVENTH or May 7th or 5-7 or 5/7<br /><br />5 and 7 Blind Spot Day Usually you Look over your right shoulder to your 5 oclock Look over your left shoulder to your 7 oclock.<br /><br /> Today Hind Sight is simplified Heinz Sight 57 to see if anyone is katching Up like whomever Hunts for instance. Perhaps on 5/7 our hind sight combines with our forward sight creating a scenario where our 5-7 oclock arc vector is carried forward to our 12 oclock straight forward vision, and our 6 oclock, our perfectly lined behind, is embraced inside this blindspot hug where we actually have our six fully forward operative..(safety sixth sense) All rearview vision and standard vision become co-linear, or multi-linear, extra-linear, or super-linear, which brings us to this Proof<br /><br /> Heinze = Henry = Heinrich = Holy Moly His first and last name are both the same his name is Henry Heinze why is this bizarre task turning out scary successful right now. The etymological origin of Henry and Heinz as they are one and the same word in German and English --- means Ruler (Ruling Class) or to move in a linear fashion or to measure, like a straight forward ruler or like a Ruler or a Euler(trying a math joke) ;-). This is absolute proof that 57 is chosen by Linear Henry Hindsight to these Military coordinates of 5oclock and 7oclock. Especially with the catch up, which signifies someone behind either catching up from behind or falling behind but still under rearview supervision. I consider this astonishingly successful core discovery of the root energy behind the variables I am investigating.... and in real time and which are very unusual proofs for some people out there and I understand that, but the intellect is forced to engage, or otherwise be lost and fade away into irrelevance so lets get real. This is real youre in a corner now if you want to gaslight your way out of this one feel free because this is wildly solid clustering of evidences mounting beyond the levels of dismissals.<br /><br /> All the road becomes one, and then I think radians mustard come into play here because isn't a radian equal to 57.2958Â°degrees with 180Â°- (a rotation from front to rear or vice versa in human directional context) -involved in the conversion equation. So here we have a radius of a circle calculated at its length properly measured, and then this exact length is reintroduced to the circumference of the very same circle it had been squared away from. they have an animation on the wikipedia for it. I don't understand Radians except for that this might be dangerous circular squaring nonsense because the remainder fraction in the 1 radian to degree conversion compounds the numbers in the fractional remainder 29 and 58 (57.2958Â°)just like when you divide our host numbers, todays host numbers, 5(month of May) by 7 (day of Tuesday). 5/7 = 0.7142857. multiples of 7 through out and also other calculation relationships exist here its a monster level scary albeit sacred collection of numbers like a diamond construct it shines and is multidimesional like a Metatrons cube. 7 14 28 57<br /><br />Toma Juniorhttps://www.blogger.com/profile/13033885169690094291noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-29798128931333693012024-05-04T01:39:27.441+01:002024-05-04T01:39:27.441+01:00I have checked the referenced article by Nicholson...I have checked the referenced article by Nicholson and find that my assertion is correct. Nicholson uses (n+1), our p, as the prime number and asserts that the division property applies when the power x, or n in our notation, x<n. Or in Pat's notation, n<p-1. I apologize if there is any confusion because the original article and the blog use the parameter n in different connotations. The article is available at JSTOR. There is also a biography of Nicholson in the same issue that you might find interesting.Cyehttps://www.blogger.com/profile/04769420912487587777noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-2322590910270254432024-04-30T01:23:51.186+01:002024-04-30T01:23:51.186+01:00Thank you so much for responding. I'm talking ...Thank you so much for responding. I'm talking about the power n to which p-1, p-2, etc are raised. Your demo with was with n=2. Try this with n=6, which is p-1. That is (6^6+5^6+4^6+3^6+2^6+1)/7=9595.857...<br />The blog says "divisible by p for any power n smaller than p." I'm saying, "...smaller than p-1."Cyehttps://www.blogger.com/profile/04769420912487587777noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-29904072049684629212024-04-29T23:22:08.426+01:002024-04-29T23:22:08.426+01:00Thanks, Will try to correct. https://pballew.blog...Thanks, Will try to correct. https://pballew.blogspot.com/2024/01/solving-quadratic-equations-by-analytic.htmlPat's Bloghttps://www.blogger.com/profile/15234744401613958081noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-16686002293878635512024-04-29T23:16:52.882+01:002024-04-29T23:16:52.882+01:00Thanks, Will try to correct. Thanks, Will try to correct. Pat's Bloghttps://www.blogger.com/profile/15234744401613958081noreply@blogger.com