tag:blogger.com,1999:blog-5134418801703349975.comments2017-07-07T12:09:34.483-04:00Math ArgumentsCurmudgeonhttp://www.blogger.com/profile/04323026187622872114noreply@blogger.comBlogger329125tag:blogger.com,1999:blog-5134418801703349975.post-39083514580072351472016-12-12T12:18:04.360-05:002016-12-12T12:18:04.360-05:00Technically discrete, but can be handled as contin...Technically discrete, but can be handled as continuous in statistics. (Why do we care about discrete vs continuous in statistics?)Sue VanHattumhttps://www.blogger.com/profile/10237941346154683902noreply@blogger.comtag:blogger.com,1999:blog-5134418801703349975.post-5532614135438026772016-11-03T09:33:21.361-04:002016-11-03T09:33:21.361-04:0037?37?Darren Clarkhttps://www.blogger.com/profile/04948671511430912336noreply@blogger.comtag:blogger.com,1999:blog-5134418801703349975.post-30281609275994998142016-10-26T06:02:24.660-04:002016-10-26T06:02:24.660-04:001/41/4Greghttps://www.blogger.com/profile/05719453078836590301noreply@blogger.comtag:blogger.com,1999:blog-5134418801703349975.post-90764329258445554142016-08-10T22:44:06.952-04:002016-08-10T22:44:06.952-04:00Where Did You Get 360 To Subtract From??Where Did You Get 360 To Subtract From??Unknownhttps://www.blogger.com/profile/00794332843020929531noreply@blogger.comtag:blogger.com,1999:blog-5134418801703349975.post-24059855835529274422016-07-25T15:07:52.339-04:002016-07-25T15:07:52.339-04:00If the first one has an expected value of 4.96, co...If the first one has an expected value of 4.96, could you just check the probability of player B getting a 5 or 6? I get a 96% chance of rolling at least one high die, so I would expect B to win more games.Denise Gaskinshttps://www.blogger.com/profile/11928843626113889088noreply@blogger.comtag:blogger.com,1999:blog-5134418801703349975.post-47528719667725553502016-06-16T13:35:23.694-04:002016-06-16T13:35:23.694-04:00The first is not hard to analyze. I get an expecte...The first is not hard to analyze. I get an expected value of 4.96. The 2nd was too hard to analyze for me. (Am I missing simpler ways of organizing the possibilities?) So I simulated it in Excel. (I wanted to use Python, but couldn't remember how to get started.) In Excel, I used Int(6*rand())+1, 8 columns across, for the dice roll. Then I used Large(a1:h1,2) to get the 2nd biggest. Then I copied down 1000 rows, and averaged. Copy-paste gets new random numbers. It was always between 5.1 and 5.2. So B wins more games.Sue VanHattumhttps://www.blogger.com/profile/10237941346154683902noreply@blogger.comtag:blogger.com,1999:blog-5134418801703349975.post-36803985638690022152016-04-07T12:05:47.556-04:002016-04-07T12:05:47.556-04:00niceniceAllen jeleyhttps://www.blogger.com/profile/10312119051975318074noreply@blogger.comtag:blogger.com,1999:blog-5134418801703349975.post-61311376760885460012016-02-03T17:45:07.972-05:002016-02-03T17:45:07.972-05:00Figure 3Figure 3Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-5134418801703349975.post-62193194943440476772015-12-17T17:23:57.100-05:002015-12-17T17:23:57.100-05:00True, but that's why I changed the wording. As...True, but that's why I changed the wording. As to the level, ... This is an equal opportunity argument site.Curmudgeonhttps://www.blogger.com/profile/04323026187622872114noreply@blogger.comtag:blogger.com,1999:blog-5134418801703349975.post-14417544359252278292015-12-16T17:49:20.928-05:002015-12-16T17:49:20.928-05:00RH:LH=83:17, so 83% right-handed, and 100 is the f...RH:LH=83:17, so 83% right-handed, and 100 is the fewest. This is primary school arithmetic and should be solved using LCMs, and is not a "proportion" in the usual mathematical meaning.Five Triangleshttps://www.blogger.com/profile/12846752710456413605noreply@blogger.comtag:blogger.com,1999:blog-5134418801703349975.post-14315654744221525672015-12-16T13:20:55.124-05:002015-12-16T13:20:55.124-05:00niceniceAllen jeleyhttps://www.blogger.com/profile/10312119051975318074noreply@blogger.comtag:blogger.com,1999:blog-5134418801703349975.post-75723546306628839492015-11-28T00:21:36.007-05:002015-11-28T00:21:36.007-05:001/4 th
1/4 th<br />Udayhttps://www.blogger.com/profile/01247327732457809774noreply@blogger.comtag:blogger.com,1999:blog-5134418801703349975.post-21747078848312932282015-11-07T11:31:00.944-05:002015-11-07T11:31:00.944-05:00Not related to Calculus, but a personal favourite ...Not related to Calculus, but a personal favourite anyway: what curve describes the midpoint of the ladder (or any other point in the ladder) as the top lands?JJhttps://www.blogger.com/profile/16829561981417320165noreply@blogger.comtag:blogger.com,1999:blog-5134418801703349975.post-38095338479824951552015-11-01T16:21:51.452-05:002015-11-01T16:21:51.452-05:00Choose whichever suits your students' whim. I...Choose whichever suits your students' whim. I say, sure a=b=c=2 is fine, making 64 different ways to pick the numbers. If you'd rather, do it the other way. These questions are meant to spark discussion. Maybe leave it up to the kids?Curmudgeonhttps://www.blogger.com/profile/04323026187622872114noreply@blogger.comtag:blogger.com,1999:blog-5134418801703349975.post-10555881343940413582015-11-01T15:34:29.950-05:002015-11-01T15:34:29.950-05:00Strictly speaking, $20 \div 10 \div 2$ is "no...Strictly speaking, $20 \div 10 \div 2$ is "not included in the PEMDAS order of operations" either. (Is it $1$ or $4$?) The takeaway is that, when we lose associativity, parentheses can be necessary in making an expression unambiguous.<br /><br />And so, while there may exist an accepted order of operations for a tower of exponents, it would be best to use parentheses from the outset...<br /><br />(For the actual question posed: It is not clear to me whether the numbers can be picked with repetition. Is a=b=c=2 a possibility? Etc.)mathwaterhttps://mathwater.wordpress.com/noreply@blogger.comtag:blogger.com,1999:blog-5134418801703349975.post-67741756699902910482015-10-25T10:50:35.054-04:002015-10-25T10:50:35.054-04:00I know a circle can pass through 12 points. Hmm......I know a circle can pass through 12 points. Hmm...Sue VanHattumhttps://www.blogger.com/profile/10237941346154683902noreply@blogger.comtag:blogger.com,1999:blog-5134418801703349975.post-39327258819636147332015-10-15T17:50:39.940-04:002015-10-15T17:50:39.940-04:00Yes, yes I did.
Thanks, I'll fix it.Yes, yes I did.<br />Thanks, I'll fix it.Curmudgeonhttps://www.blogger.com/profile/04323026187622872114noreply@blogger.comtag:blogger.com,1999:blog-5134418801703349975.post-72300595281948448552015-10-11T22:47:13.272-04:002015-10-11T22:47:13.272-04:00Did you mean discriminant?Did you mean discriminant?mathwaterhttps://mathwater.wordpress.com/noreply@blogger.comtag:blogger.com,1999:blog-5134418801703349975.post-80060918235258552052015-09-14T14:07:29.852-04:002015-09-14T14:07:29.852-04:00It's not a matter of one form being "bett...It's not a matter of one form being "better" or "worse" than the other; it is more a matter of which form is appropriate for the current application. When writing with pen and paper, and depending upon my audience, I generally take the equation as far as the first form. It is more concise. However, because so much of my own work involves computer programming, and needs to include the option for complex solutions, the second form often gets applied. In any situation for which the solutions cannot be assumed to be real numbers, the two terms are going to be dealt with separately, so you end using the second form. Might as well start with it in these situations.David_Bhttps://www.blogger.com/profile/04006454809807494895noreply@blogger.comtag:blogger.com,1999:blog-5134418801703349975.post-59658424635790390082015-08-30T08:31:07.491-04:002015-08-30T08:31:07.491-04:00The bottom one emphasizes the line of symmetry (fi...The bottom one emphasizes the line of symmetry (first term) and demonstrates the symmetric nature of the parabola at any pair of solutions. Nonetheless, I teach them to sing the top one.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-5134418801703349975.post-5459366629957347022015-08-23T14:21:37.586-04:002015-08-23T14:21:37.586-04:00personally, i think ±sqrt(-c/a+(b/(2a))^2)-b/(2a) ...personally, i think ±sqrt(-c/a+(b/(2a))^2)-b/(2a) is best. (Historical/geometric completing the square).<br /><br />I don't really like either of the two above, but of the two above, I prefer the bottom one, because it's very slightly easier to use it to talk about the location of the vertex being the arithmetic mean of the roots.<br /><br />My students, though, hate it when I use the bottom one. They're all used to the top one. I think that says something about how they've learned algebraic equivalence, but I'm not going to dwell on it here.<br /><br />-Carlos (g+ sign in isn't working for me).Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-5134418801703349975.post-552213662911781812015-08-23T08:17:23.374-04:002015-08-23T08:17:23.374-04:00Better for what purpose? They'll get you the s...Better for what purpose? They'll get you the same answer. The top one is easier to remember; the bottom one will get you to the final conventional form faster when the root is irrational. So for teaching, I'd say the top one is usually better, but for mathematical practice the bottom one is probably better.paulhartzerhttps://www.blogger.com/profile/02150147778452779078noreply@blogger.comtag:blogger.com,1999:blog-5134418801703349975.post-42851040941449996282015-08-23T00:44:25.247-04:002015-08-23T00:44:25.247-04:00I imagine either can be of use. I've always us...I imagine either can be of use. I've always used the top one.Sue VanHattumhttps://www.blogger.com/profile/10237941346154683902noreply@blogger.comtag:blogger.com,1999:blog-5134418801703349975.post-78736599844391336262015-08-22T22:20:43.209-04:002015-08-22T22:20:43.209-04:00Our standard answer: it depends. In solving the f...Our standard answer: it depends. In solving the following quadratic equation exercise, it's not immediately clear which format would be "better" (or maybe neither is useful):<br />https://docs.google.com/document/d/1GSwHvywSXMhYI4yofkFbfV13TzZ-fQ1OVpHOTs3bv1A/editFive Triangleshttps://www.blogger.com/profile/12846752710456413605noreply@blogger.comtag:blogger.com,1999:blog-5134418801703349975.post-86103887530743018522015-07-16T23:06:58.340-04:002015-07-16T23:06:58.340-04:00Consider the game in which two players alternate p...Consider the game in which two players alternate placing quarters on a large square table. The rules are that your quarter must be placed down fully on the table; no overlapping with others, and no hanging off of the edge. The first player to have no legal move loses.<br /><br />The game described above can be won by Player 1: Take the center point on move one, and then mirror the opponent's moves thereafter.<br /><br />This is a more general "strategy-stealing" idea, but it can be applied to the game at hand, too:<br /><br />Player 1 should pick 5, and, thereafter, mirror their opponent's n by picking 10-n.<br /><br />See also: http://math.stackexchange.com/a/366088mathwaterhttps://mathwater.wordpress.com/noreply@blogger.com