tag:blogger.com,1999:blog-5811124440838283502.comments2017-07-28T10:32:41.994+01:00Tony's Maths BlogTonyhttp://www.blogger.com/profile/08832715837375830128noreply@blogger.comBlogger134125tag:blogger.com,1999:blog-5811124440838283502.post-70804200239391451122017-07-25T19:02:00.818+01:002017-07-25T19:02:00.818+01:00Yes, my mistake. I should have referred to absolu...Yes, my mistake. I should have referred to absolute values.Tonyhttps://www.blogger.com/profile/08832715837375830128noreply@blogger.comtag:blogger.com,1999:blog-5811124440838283502.post-32510125041828632982017-07-25T17:41:09.251+01:002017-07-25T17:41:09.251+01:00Actually -0.414 is greater than -1/2, not less tha...Actually -0.414 is greater than -1/2, not less than.Johnhttps://www.blogger.com/profile/06873501610477076216noreply@blogger.comtag:blogger.com,1999:blog-5811124440838283502.post-60096537160192508972017-02-16T12:46:37.480+00:002017-02-16T12:46:37.480+00:00"seeing better people than me make errors is ..."seeing better people than me make errors is encouraging: I make lots of mistakes and it's helpful to realise that most other people do too!"<br /><br />This is so true! After all, we all learn from our mistakes. It's up to us if we look at our mistakes as a total let-down or as milestones on achieving greater things. :) Great post, Tony :)<br /><br /><br /><a href="https://classesatoz.co.uk/" rel="nofollow">Classes A-Z UK</a>mizukikahochihttps://www.blogger.com/profile/10665079651256770924noreply@blogger.comtag:blogger.com,1999:blog-5811124440838283502.post-62854527769370577812017-01-04T01:02:10.268+00:002017-01-04T01:02:10.268+00:00Wasn't Gauss a rather arrogant and cantankerou...Wasn't Gauss a rather arrogant and cantankerous man, Newton, Nash...The Abstracthttps://www.blogger.com/profile/16612677287157201655noreply@blogger.comtag:blogger.com,1999:blog-5811124440838283502.post-65052197568372298882017-01-03T04:54:01.460+00:002017-01-03T04:54:01.460+00:00Sie non errasset, fecerat ille minus.
Christian Go...Sie non errasset, fecerat ille minus.<br />Christian Goldbach wrote this to Leonhard Euler in 1742:<br /><br />“when I recently reconsidered the supposed sums of the two series mentioned at the end of my last letter, I perceived at once that they had arisen by a mere writing mistake. But of this indeed the proverb says “If he had not erred, he should have achieved less”; for on that occasion I came upon the summations of some other series which otherwise I should hardly have looked for, much less discovered.”<br /><br />This letter sparked Euler’s interest in the ζ-function.Unknownhttps://www.blogger.com/profile/08091306578217271112noreply@blogger.comtag:blogger.com,1999:blog-5811124440838283502.post-25185051829438772692016-12-30T07:43:45.021+00:002016-12-30T07:43:45.021+00:00..isn't it more likely that the author had fac.....isn't it more likely that the author had factored in the unpredictability of cats? The real answer is a random number. Probably. vanilla beerhttps://www.blogger.com/profile/02522374087781244148noreply@blogger.comtag:blogger.com,1999:blog-5811124440838283502.post-61365240415718692812016-11-15T20:47:04.942+00:002016-11-15T20:47:04.942+00:00It is curious where a passion/enjoyment stems from...It is curious where a passion/enjoyment stems from. I've always thought that it is most probably due to a positive reaction from a parent or loved person in a young childs life. It wouldn't take a lot to inspire the child to practice the art/subject more, thus improving the skill or perceived "talent" and the virtuous cycle rotates and rotates...<br /><br />As a sidenote to the above, have you ever thought whether something you enjoy (mathematics or otherwise) is as a result of indirect (or direct) manipulation on somebody's behalf? (parent/relation) Samnoreply@blogger.comtag:blogger.com,1999:blog-5811124440838283502.post-4920073405570740982016-03-21T10:47:39.891+00:002016-03-21T10:47:39.891+00:00nice blog. http://www.amaabacus.com/nice blog. http://www.amaabacus.com/Surendra mahawarhttps://www.blogger.com/profile/05793721302326915950noreply@blogger.comtag:blogger.com,1999:blog-5811124440838283502.post-44714692745894030512016-03-03T22:27:08.134+00:002016-03-03T22:27:08.134+00:00Be realistic- math sucks and everyone really hates...Be realistic- math sucks and everyone really hates it.<br /><br />Most math teachers have no personality, which seems to be a requirement to be one.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-5811124440838283502.post-15979190942948668032016-02-02T18:12:47.875+00:002016-02-02T18:12:47.875+00:00Thx for this, glad I'm not the only one to hav...Thx for this, glad I'm not the only one to have suspected maths to have anti-arrogance properties. I'll do my best to take my maths courses as a work on myself, on my faults, from this moment on.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-5811124440838283502.post-59611866977873559702015-10-26T14:03:45.406+00:002015-10-26T14:03:45.406+00:00I thinks they just didn't expect that to occur...I thinks they just didn't expect that to occur and simply failed to take into account.Australian lotto resultshttp://australian-lotto-results.com/noreply@blogger.comtag:blogger.com,1999:blog-5811124440838283502.post-62957064615041443522015-08-02T15:09:14.644+01:002015-08-02T15:09:14.644+01:00Thank you for your reply Tony. Much appreciated.Thank you for your reply Tony. Much appreciated.Alastair Batemanhttps://www.blogger.com/profile/14395447443056931757noreply@blogger.comtag:blogger.com,1999:blog-5811124440838283502.post-40118231256762156822015-08-01T16:04:29.857+01:002015-08-01T16:04:29.857+01:00Alastair,
Thank you for your observations.
1) I ...Alastair,<br /><br />Thank you for your observations.<br /><br />1) I agree that the existence of the intersections is obvious, but it doesn't follow from Euclid's five axioms. But I don;t think anybody seriously worried about this for a couple of thousand years!<br />2) It's a long time since I looked at the Kepler conjecture so I can't really comment.<br />3) We need to wait longer: de Branges' proof is sketchy and as far as I know has not so far been disproved.<br />4) Again not my area, I'm afraid.Tonyhttps://www.blogger.com/profile/08832715837375830128noreply@blogger.comtag:blogger.com,1999:blog-5811124440838283502.post-21227552003809979292015-08-01T12:25:32.962+01:002015-08-01T12:25:32.962+01:00Having only just read the content of your lecture ...Having only just read the content of your lecture 'Proof by Computer & Proof by Human' which I found very interesting, at least those parts of it that I could assimilate, I would like to make the following observations. <br />[1] My mind fails to see any gap in Euclid's proof of his Proposition 1 since the construction of two circles of equal radius, the second of which is centred on the circumference of the first logically results in their intersection at 2 places so that any additional embellishments to prove they intersect are in my opinion and I would suspect that of most other persons, simply superfluous.<br />[2] I totally fail to understand all the hype surrounding 'Kepler's Sphere Packing Problem'. In an infinite array of spheres in the close packed hexagonal configuration any 1 sphere is in contact with 6 spheres in a hexagonal array around it's equator and 3 contacting spheres around its north pole and a further three around the south pole, a total assembly of 13 contacting spheres. Now all the centres of the contacting spheres can be joined by a straight line passing through the point of contact equal to the diameter of the spheres. To increase the density of packing a 14th sphere would have to be introduced so pray tell me where? To me it beggars belief that after 400 years it takes a computer using 5000 configurations to be just 99% sure that the closed packed structures are indeed the best possible assemblage. Where on earth did he get 5000 different configurations from when there are at most 7? basic arrangements for the atoms in any crystal found in nature and atoms are virtually empty space and the close packed hexagonal /face centred cubic are indeed the densest assemblage!<br />[3] That Lois de Branges claim to have proved 'The Riemann Hypothesis' made it into 'The Guardian' newspaper where a celebrity Oxford professor was sceptical that it was indeed the proof. He considered that the proof of 'TRH' could eventually result in a 'prime spectrometer' and bring e-commerce to its knees since security base on RSA would be compromised. As security has not yet been compromised do we take it that Lois de Branges has not proved 'T.R.H.' and is this then 'proof/ disproof by consequent outcomes' or do we need to wait a bit longer before drawing a conclusion?<br />[4] Finally what should one do if they find a simple proof that everyone says does not and cannot exist yet every fibre of their being tells them it is correct? Seek psychiatric help, commit suicide or seek the opinion of a mathematician?<br />For example if we take the following algebraic identity z^n = y^n + x^n we can ask the question what values if any of n result in an all integer solution. <br />[Step 1] Multiply the equation by z^n to give (z^n)^2 = (z.y)^n + (z.x)^n <br />[Step 2] Multiply the equation by (z^n)^2 to give (z^(2n))^2 = (z^3.y)^n + (z^3.x)^n <br />[Step 3] Multiply the equation by (z^n)^2 to give (z^(3n))^2 = (z^5.y)^n + (z^5.x)^n <br />[Step 4] Multiply the equation by (z^n)^2 to give (z^(4n))^2 = (z^7.y)^n + (z^7.x)^n and so AD INFINITUM.<br />Now every (integer)^2 can be split into the 'difference of two squares' and re-arranged to produce a 'Pythagorean Triple' which for the infinity of odd integers are all primitive (Pythagorean series) and for the even integers are primitive for all (integer)^2 MOD 8 = 0 (Platonic series).<br />I can therefore only draw the conclusion that the equation z^n = y^n + x^n has a one to one correspondence with the 'Pythagorean Triples' so the only conceivable value for n is 2 and so any higher value for n would be an absurdity . QED.<br />I have loaded the bullet into the chamber.<br />I have spun the chamber.<br />There is a bullet in the firing position if the proof is FALSE.<br />There is no bullet in the firing position if the Proof is TRUE.<br />CLICK!! AM I DEAD OR ALIVE.<br />Alastair Batemanhttps://www.blogger.com/profile/14395447443056931757noreply@blogger.comtag:blogger.com,1999:blog-5811124440838283502.post-42546882876666771412015-06-30T17:20:47.012+01:002015-06-30T17:20:47.012+01:00I like the valuable information you provide in you...I like the valuable information you provide in your articles.<br />It was really a wonderful article and I was really impressed by reading this blog.<br /><a href="http://www.btechdistanceeducationinindia.com" rel="nofollow">B.Tech | MBA | MCA | Diploma | Distance Learning Program</a><br />B.Tech Distance Education chennaihttps://www.blogger.com/profile/04189159793731617376noreply@blogger.comtag:blogger.com,1999:blog-5811124440838283502.post-77586636778398692212015-06-20T05:40:49.240+01:002015-06-20T05:40:49.240+01:00The photo below shows a wall of "doodles"...The photo below shows a wall of "doodles" by visitors, showing that all such doodles (formed by closed curves) can be coloured in only two colours so that regions with a common boundary are different colours.<a href="http://www.constellationsrecovery.com/residence/" rel="nofollow">sober living nyc</a>jowdjbrownhttps://www.blogger.com/profile/09633259957714692411noreply@blogger.comtag:blogger.com,1999:blog-5811124440838283502.post-58202883506469474822015-05-24T21:19:10.845+01:002015-05-24T21:19:10.845+01:00Thanks for your comment. First of all, I am certa...Thanks for your comment. First of all, I am certainly not the greatest mathematician in the world (do I want to be? I'm not sure!) <br />I think the argument is that if we have two statements, A which says "A and B are both false" and B which can be anything you like, then the only consistent arrangement is that B is true and A is false. Then A is indeed false, because it is not true that both statements are false, since B is not false. But any other arrangement leads to a contradiction. Thus the argument appears to prove that B must be true (even if B is complete nonsense). Which is a little worrying.Tonyhttps://www.blogger.com/profile/08832715837375830128noreply@blogger.comtag:blogger.com,1999:blog-5811124440838283502.post-48104668239444577452015-05-08T04:07:56.530+01:002015-05-08T04:07:56.530+01:00Good evening!!
I just watched your lecture on you ...Good evening!!<br />I just watched your lecture on you tube, <br />I have a bit of a question, please help me if you have a moment?!?<br /><br />You said:<br /><br />"A: Both these statements are False<br />"B: I am the greatest mathematician in the world".<br /><br />"If B is false, then A would be true, yet A states in itself that it is False, so we have a contradiction."<br />"But, If B is true, then A would be false, just as A says it is false, so we have no contradiction if B is True. Thus: B must be true."<br /><br />Now, I don't see how this escapes the paradox, nor does it avoid contradiction....<br /><br />For:<br /><br />If B is FALSE, then A would be true, and if A is true, A then becomes false. If A is then decided to be false, it is actually true, and on and on.....<br /><br />If B is TRUE, then A would actually be false, which is exactly what A says it is, so therefore A would be true, but if A is true, then it is false, and when A becomes false, we know then that it is true...and on and on and on again....<br /><br />This doesn't seem to escape the contradiction. This is really just a pesky liar paradox hanging around and imposing itself upon another statement. <br /><br />A paradoxical statement, which is both self-referential and referential to another non-self-referential statement, one who's truth or falsehood depends on the same of the paradoxical latter, only leaves us with the inability to determine anything about either statement. We remain (by either begining or ending) in a cyclical loop of uncertainty within the first sentence, thus not being able to decide anything about the validity of the second. <br /><br />You claim this example escapes the contradiction, with the only logical answer being that "B is true". I do see how you got here, but I don't see how it can stop here.<br /><br />At the same point that we decide that you ARE actually the greatest mathematician in the world, the first statement instantly becomes false, which then, by it's own self-proclamation of it's falsity, makes it true, so then in turn it makes us realize that you are no longer the greatest mathematician in the world....(no worries, keep going and you'll be back to the greatest again, in @ half a second.)<br /><br />Please correct me here, or explain if I am wrong?<br /><br />What I think is that logic itself is self-referential. <br />You want to be the greatest mathmatician in the world, (maybe you are? Who knows!) but because this is your identity, this is where reasoning ends. <br /><br />Maybe no self-referential system, which makes claims of it's own truth or falsehood, should be trusted to determine anything for certain about elemets of either itself or outside of it? <br /><br />The Bible, Science, and reason itself, all seem to do this. <br />Oh dear, now what? <br /><br />Certain uncertainty!!<br /><br />I've never studied logic, but this sure is fun!<br /><br /><br />Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-5811124440838283502.post-10204695128435103842015-03-28T05:13:59.715+00:002015-03-28T05:13:59.715+00:00Try this one now: FOUR vampires and FOUR maidens a...Try this one now: FOUR vampires and FOUR maidens are at the foot of a tall building and wish to get to the bar on the top floor. The lift only holds THREE people (for convenience we class vampires as people), and needs one person to operate it. If ever the vampires outnumber the maidens at any place, they will do something unspeakable. How can the vampires and maidens all safety get to the top? Navam Pakianathanhttps://www.blogger.com/profile/04870526855658819024noreply@blogger.comtag:blogger.com,1999:blog-5811124440838283502.post-27936224225481129532015-02-24T14:55:04.765+00:002015-02-24T14:55:04.765+00:00Very nice blog, this blog is helping lot of curiou...Very nice blog, this blog is helping lot of curious minds in all over world, i agree your blog articles are highly informative written after deep research and thinking, keep writing such article forever, i hope your site visitors may use the shared information on this <a href="http://sqrt.in" rel="nofollow">quiz site</a>, its a great site where you can use all your knowledge to participate in quiz and compete with other users, you must give a look onto it. IMPETUShttps://www.blogger.com/profile/00328295045124730459noreply@blogger.comtag:blogger.com,1999:blog-5811124440838283502.post-27990146047988499002015-02-13T01:43:23.164+00:002015-02-13T01:43:23.164+00:00I've just come across this. Interesting. I not...I've just come across this. Interesting. I note you use the possible conditional, 'if my cup were...' This seems to imply that 'infinitely far' is a possible concept - do you really mean that?Tony Vnoreply@blogger.comtag:blogger.com,1999:blog-5811124440838283502.post-65590914741167254762014-09-21T01:38:59.307+01:002014-09-21T01:38:59.307+01:001. VM up
2. M down
3. V up
4. 0 Down
5. MM up
6 O ...1. VM up<br />2. M down<br />3. V up<br />4. 0 Down<br />5. MM up<br />6 O down<br />7 VM up<br /><br />Unless I missed the rules about people have to come downAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-5811124440838283502.post-8443364685153397152014-09-18T13:50:31.711+01:002014-09-18T13:50:31.711+01:00Ah yes. I was solving it like the wolf, goat and c...Ah yes. I was solving it like the wolf, goat and cabbage one, like the maiden was only in danger if you left her there for a turn. Ok, thanks :)Jen Quinnnoreply@blogger.comtag:blogger.com,1999:blog-5811124440838283502.post-49709674775228563262014-09-13T11:54:43.573+01:002014-09-13T11:54:43.573+01:00Ah yes. I was solving it like the wllf, goat and c...Ah yes. I was solving it like the wllf, goat and cabbage one, like the vampires would only kill if LEFT with fewer maidens. I see, thanks :)Jen Quinnnoreply@blogger.comtag:blogger.com,1999:blog-5811124440838283502.post-46687623278793570532014-09-13T08:53:23.204+01:002014-09-13T08:53:23.204+01:00Jen - I'm afraid that after step 3 you have tw...Jen - I'm afraid that after step 3 you have two vampires and one maiden at the top. Anon- there is the same issue with the proposal you mention.Tonyhttps://www.blogger.com/profile/08832715837375830128noreply@blogger.com