tag:blogger.com,1999:blog-3748625510348961342.comments2018-10-30T07:43:37.353-07:00solidangl.esBill Shillitohttp://www.blogger.com/profile/17774101901445053590noreply@blogger.comBlogger42125tag:blogger.com,1999:blog-3748625510348961342.post-18379222109003167302018-10-30T07:43:37.353-07:002018-10-30T07:43:37.353-07:00Thanks for a very interesting blog. What else may ...Thanks for a very interesting blog. What else may I get that kind of info written in such a perfect approach? <a href="http://flooringinstaller.ca/" rel="nofollow">laminate flooring</a><br />Ella lilyhttps://www.blogger.com/profile/10148028990041792924noreply@blogger.comtag:blogger.com,1999:blog-3748625510348961342.post-48419608841953953122018-10-23T13:18:07.620-07:002018-10-23T13:18:07.620-07:00Wow! Sounds interesting! It proves that developmen...Wow! Sounds interesting! It proves that development of skills needed to successfully complete mathematic assignments is not limited to the numerous perplexing books. To improve my knowledge in math I also use this service <a href="https://www.assignmentexpert.com/math" rel="nofollow">https://www.assignmentexpert.com/math</a>. From algebra through tensor analysis, their team of experts helps me with the highest quality work that puts me back on track to succeed in my math classes. Timely delivery, reasonable prices, and proper formatting. What else does a student need?Russel Shermanhttps://www.blogger.com/profile/15589072811536668847noreply@blogger.comtag:blogger.com,1999:blog-3748625510348961342.post-22618964839282006662018-10-03T04:54:06.081-07:002018-10-03T04:54:06.081-07:00Thanks for info!Thanks for info!Richard Dolanhttps://www.blogger.com/profile/04613150274857338834noreply@blogger.comtag:blogger.com,1999:blog-3748625510348961342.post-59675803824458947692018-09-24T23:37:59.498-07:002018-09-24T23:37:59.498-07:00Ah - you are dealing with value creation, and you ...Ah - you are dealing with value creation, and you have just encountered the critical issue of 'synergy.' You might care to address the issues of maths, economics and value creation some time (gaining a Nobel Prize for progressing us beyond Adam Smith and Karl Marx in the process).John Hudsonhttps://www.blogger.com/profile/11013377373368699963noreply@blogger.comtag:blogger.com,1999:blog-3748625510348961342.post-6075066974529262182018-09-21T18:54:18.410-07:002018-09-21T18:54:18.410-07:00I'm apparently very late to the party but I ab...I'm apparently very late to the party but I absolutely love this idea. I came up with some really nice LaTeX code for it:<br />\raisebox{\depth}{\scalebox{1}[-1]{$\sqrt[\raisebox{\depth}{\scalebox{1}[-1]{\tiny{2}}}]{\raisebox{\depth}{\scalebox{1}[-1]{16}}}$}}Iyan Siwikhttps://www.blogger.com/profile/06005006477287388259noreply@blogger.comtag:blogger.com,1999:blog-3748625510348961342.post-85257515058070226092018-09-18T13:42:12.627-07:002018-09-18T13:42:12.627-07:00Hey Bill. Might want to delete that spam comment.Hey Bill. Might want to delete that spam comment.Quintopiahttps://www.blogger.com/profile/11935053984682797775noreply@blogger.comtag:blogger.com,1999:blog-3748625510348961342.post-6842715464504968852018-09-18T13:41:13.770-07:002018-09-18T13:41:13.770-07:00Hey Bill. Might want to delete that spam comment.Hey Bill. Might want to delete that spam comment.Quintopiahttps://www.blogger.com/profile/11935053984682797775noreply@blogger.comtag:blogger.com,1999:blog-3748625510348961342.post-23532624803188090332018-04-24T13:15:07.983-07:002018-04-24T13:15:07.983-07:00I'm not sure where you're getting your inf...I'm not sure where you're getting your information, but great topic. I needs to spend some time learning much more or understanding more. Thanks for great information I was looking for this information for my mission. <a href="https://loginmaker.org/yahoo/" rel="nofollow">yahoo sign in</a> Stefan Forgehttps://www.blogger.com/profile/09139556944706223927noreply@blogger.comtag:blogger.com,1999:blog-3748625510348961342.post-22406083989848418652018-02-12T23:47:58.559-08:002018-02-12T23:47:58.559-08:00Welcome back! I hate these things too. And I don&#...Welcome back! I hate these things too. And I don't even have the option not to teach them. Quintopiahttps://www.blogger.com/profile/11935053984682797775noreply@blogger.comtag:blogger.com,1999:blog-3748625510348961342.post-1012266931130571012017-12-21T13:23:08.447-08:002017-12-21T13:23:08.447-08:00I love your symbol, and will start using it next s...I love your symbol, and will start using it next semester. I made a bit of Latex code for "log base 2 of 8": \raisebox{.7mm}{\reflectbox{\rotatebox[origin=c]{180}{\Large{$\sqrt{~~}$}}}}$\hspace{-.6cm}{\mbox{\tiny 2}}\hspace{.2cm} 8$<br /><br />To see the compiled image: https://drive.google.com/file/d/1zYqnIFDfsrO-MMQCjI09m_rwmQhqIUfj/view?usp=sharingLynne Ipiñahttps://www.blogger.com/profile/02298838629222120903noreply@blogger.comtag:blogger.com,1999:blog-3748625510348961342.post-29002947766656199212017-11-29T19:13:05.351-08:002017-11-29T19:13:05.351-08:00I'm not sure any computer scientist would cons...I'm not sure any computer scientist would consider it more natural than e, it's just useful for many purposes.J Carrhttps://www.blogger.com/profile/03209130188845063324noreply@blogger.comtag:blogger.com,1999:blog-3748625510348961342.post-25810353847439488272017-11-29T10:18:12.483-08:002017-11-29T10:18:12.483-08:00One can’t be prepared for every scenario that can ...One can’t be prepared for every scenario that can cause havoc to one’s home or business. However it’s always good to have a plan for what to do if the inevitable happens. Especially if you live in a flood zone.<a href="https://www.flooddoctorva.com/" rel="nofollow">flooded home repair in Fairfax Virginia</a><br />Keith A. Granthttps://www.blogger.com/profile/00604416881303909732noreply@blogger.comtag:blogger.com,1999:blog-3748625510348961342.post-5424593843439501732017-10-01T20:38:50.819-07:002017-10-01T20:38:50.819-07:00This comment has been removed by a blog administrator.Hendrik Friedheimhttps://www.blogger.com/profile/02406708488103925325noreply@blogger.comtag:blogger.com,1999:blog-3748625510348961342.post-26644066691633581212016-12-31T10:34:22.028-08:002016-12-31T10:34:22.028-08:00Excellent article! I'd like to see you extend ...Excellent article! I'd like to see you extend the examples to include division and multiplication as well. It may be difficult to deal with division as something that's simple to understand as shorthand for something. 6 / 2 is short hand for 6 * 1/2 but students certainly are not used to that view. And the notion of left to right is important to include as a 3rd thing to remember since subtraction and division are not commutative.<br /><br />Bob Orchardhttps://www.blogger.com/profile/12615009252327101120noreply@blogger.comtag:blogger.com,1999:blog-3748625510348961342.post-91934163931358797822016-12-26T03:02:04.392-08:002016-12-26T03:02:04.392-08:00I hate to say this but what is the ACTUAL function...I hate to say this but what is the ACTUAL function to solve the problem you propose because the problem in today's world is no one has a FUNCTION to solve problems efficiently.Amuro Kazamahttps://www.blogger.com/profile/17142044174072293847noreply@blogger.comtag:blogger.com,1999:blog-3748625510348961342.post-48773914876427939792016-06-29T21:41:36.795-07:002016-06-29T21:41:36.795-07:00Why stopping at the + x exp relation, why not keep...Why stopping at the + x exp relation, why not keep going the pattern with the relations due the Conway chained arrow notation? With these simple relations, computation of the V of parallel wires was obtained, it was something nice! Maybe something deeper may happen if the system is generalized.Daniel de França MTd2https://www.blogger.com/profile/01281817409696805377noreply@blogger.comtag:blogger.com,1999:blog-3748625510348961342.post-9382962772830697412016-02-02T18:26:11.335-08:002016-02-02T18:26:11.335-08:00I just ran it to this post via another website. I...I just ran it to this post via another website. I am glad to see an article about alternatives to PEMDAS. For several years, I stopped using PEMDAS in my sixth grade classroom and their misconceptions like adding before all subtraction, went away completely. Well, until one of the kids came to class having his older brother help him with his homework. Suddenly he was making so many mistakes. I asked him what his brother did to "help" him and he answered "PEMDAS." I recently got all the other teachers at my school onboard with dropping PEMDAS and our scores on order of operations went up tremendously. I didn't know anyone else used GEMA. Again, like you said, it really isn't necessary to use any mnemonic at all, but it was the only way to get some to drop PEMDAS. Lovely article!LD Helferhttps://www.blogger.com/profile/15362613994636151867noreply@blogger.comtag:blogger.com,1999:blog-3748625510348961342.post-13261392684388020082015-11-14T12:02:54.975-08:002015-11-14T12:02:54.975-08:00As the author wisely noted at the end of his artic...As the author wisely noted at the end of his article, it never hurts to have too many parentheses! <br />/Bravo, --problem eliminated!Lonewolf™https://www.blogger.com/profile/17592367417704960634noreply@blogger.comtag:blogger.com,1999:blog-3748625510348961342.post-31773975960037273592015-08-16T09:00:27.189-07:002015-08-16T09:00:27.189-07:00Love it!Love it!Paul Ohttps://www.blogger.com/profile/06294340052733992008noreply@blogger.comtag:blogger.com,1999:blog-3748625510348961342.post-18584089043896129122015-05-20T14:16:29.116-07:002015-05-20T14:16:29.116-07:00A computer scientist might argue "2" is ...A computer scientist might argue "2" is the "natural" logarithm base (anything binary). <br /><br />PS: damn this commenting system is weird.Victor Hernandeshttps://www.blogger.com/profile/00064218464586434649noreply@blogger.comtag:blogger.com,1999:blog-3748625510348961342.post-66242648144597530652015-04-29T18:21:13.317-07:002015-04-29T18:21:13.317-07:00Interesting idea, but I'm not at all a fan of ...Interesting idea, but I'm not at all a fan of that "visual cancellation rule" as phrased. There's no real mathematical reason behind it - it's all smoke and mirrors, which is pedagogically dangerous. You're relying on the "b^\b^" resembling a fraction that "cancels" to be 1, after which a multiplication sign magically appears next to the exponent. Math should be logical, not magical. Cancelling things is ubiquitous, sure, but you have to know *why* it works.<br /><br />That being said, I would be interested in seeing a linear form of the radical symbol and my reflected version of it.Bill Shillitohttps://www.blogger.com/profile/17774101901445053590noreply@blogger.comtag:blogger.com,1999:blog-3748625510348961342.post-25252635717616844032015-04-29T17:42:35.800-07:002015-04-29T17:42:35.800-07:00Great idea. I had been searching for a notation t...Great idea. I had been searching for a notation that could be "typed" in linear text form. To that end, I had played around with combinations of the caret ^ and forward and reverse diagonals / \<br /><br />Given the linear notation for power:<br /><br />Power: b ^ e = p<br /><br />For root, I suggest the symbol ^/ (caret, slash):<br /><br /> p ^/ e = (b^e) ^/ e = b<br /><br />My root notation represents an "abbreviation" of the identity: e-th root of p equals p to the power 1/e,<br />that is: (b^e) ^/e represents (b^e) ^ (1/e) = b ^ (e * 1/e) = b ^ 1 = b<br /><br />But to get this advantage, I must reverse the order of base and power in the traditional notation.<br /><br />So, in similar vein, your log symbol could be represented by the symbol: ^\ (caret, back-slash):<br /><br />log: logb(p) = b ^\ p = b^\ (b^e) = e<br /><br />This is suggestive of a "visual cancellation rule" <br />b^\ (b^ e) "equals" ( b^ \ b^) e "equals" 1 * e = e.Joseph Austinhttps://www.blogger.com/profile/11397759210330425019noreply@blogger.comtag:blogger.com,1999:blog-3748625510348961342.post-40938453703237601762015-04-28T16:50:42.594-07:002015-04-28T16:50:42.594-07:00My only problem with the new notation stems from t...My only problem with the new notation stems from the laziness of the writer. Since 2 is the most natural root and e is the most natural base for logarithms, we don't bother writing the 2 when we take the square root or writing the e when we take logarithm base e (whether you denote this as log or ln is a matter of preference). It wouldn't make sense to compromise on which should be considered natural for both notations since the e^th root doesn't naturally come up and log base 2 doesn't come up much (except maybe in computer applications). I could see how there would be confusion as to why leaving the number off when the sign is in one direction implies something different than leaving the number off when the sign is in the other direction.<br /><br />That said, I like this idea and think the advantages that you explained outweigh this disadvantage.Robert Williamshttps://www.blogger.com/profile/08525366375056584669noreply@blogger.comtag:blogger.com,1999:blog-3748625510348961342.post-38437970010485462222015-04-27T21:19:44.643-07:002015-04-27T21:19:44.643-07:00The commentary here which compares implicit multip...The commentary here which compares implicit multiplication with function notation brings to mind another possible adjustment of notation. In particular, as Eric Schecter pointed out long ago (http://www.math.vanderbilt.edu/~schectex/commerrs/), the fact that these two things appear so similar leads to even more insidious errors.<br /><br />For instance, 2(x+y)=2*x+2*y is just fine. But sin(x+y)=sin(x)+sin(y) is not. It's no surprise that this mistake is common among math students though, on account of how the parentheses are, as you noted, overloaded.<br /><br />I would propose that the obviously solution is simply to quit enclosing function arguments with parentheses. Just stop overloading them, and the problem should go away.<br /><br />But how? We could switch to square brackets. In fact, we already use them for this in probability and statistics for some reason. For instance, with expectation: E[X+Y]. Oddly enough, though, expected value is the one commonly used named function that IS linear. E[X+Y]=E[X]+E[Y] is true. I have no idea why we've decided not to use parentheses in this case. Anyway, it sets a precedent that we should follow with all functions.<br /><br />Right now, a student could be quite nonplussed when his teacher goes bananas over his trying to do things like sin(x+y)=sin(x)+sin(y), but if it were sin[x+y], perhaps he would be more cautious, thinking, "OMG SQUARE BRACKETS I BETTER BE CAREFUL IT MAY NOT BE A LINEAR FUNCTION!"<br /><br />There is one place where his caution would still not help him, however. He would still be susceptible to the Freshman's Dream. Exponents are not currently written using function notation, even though they perform a decidedly non-linear operation. Because of this even if we committed to using square brackets for function arguments, we'd still write (x+y)².<br /><br />Come to think of it, isn't exponentiation the only operator in high school math books that is applied on the right? The only one that is right-associative? I'm starting to doubt the sanity and utility of exponent notation. But that's a completely different argument...Quintopiahttps://www.blogger.com/profile/11935053984682797775noreply@blogger.comtag:blogger.com,1999:blog-3748625510348961342.post-78115844630824381482015-04-27T18:59:55.327-07:002015-04-27T18:59:55.327-07:00"literally pointing to the part we're loo..."literally pointing to the part we're looking for in the corresponding exponential expression"<br /><br />Yes, yes, and again yes! This is exactly what I meant. Glad to see that others are understanding why I chose this notation.<br /><br />If you feel this should be a thing, please share it with whoever you think may be interested!Bill Shillitohttps://www.blogger.com/profile/17774101901445053590noreply@blogger.com