tag:blogger.com,1999:blog-5303307482158922565.comments2024-10-14T13:29:20.221-07:00Math Mama Writes...Sue VanHattumhttp://www.blogger.com/profile/10237941346154683902noreply@blogger.comBlogger2073125tag:blogger.com,1999:blog-5303307482158922565.post-14831496577787154252024-09-22T06:30:44.369-07:002024-09-22T06:30:44.369-07:00Love this post. I first encountered this type of ...Love this post. I first encountered this type of wall when visiting University of Virginia, but did not know about the term “Crinkle Crankle Wall,” or the mathematical reasons for its geometric material resource efficiency relative to a straight wall. It is one thing to prove that a sinusoidal wall is stronger than a straight wall using the same amount of material, but how do we prove that a sinusoidal wall is more efficient than almost any other conceivable smooth shape? (E.g. imagine a wall composed of parabolic or elliptical or any other shape you can think of segments joined together, with the proviso that the functions describing the shapes be reasonably “smooth”.). That would be a problem in the Calculus of Variations, which is beyond the curriculum of second year calculus. (Operationally, theorems in Calculus of Variations generally assume that “smooth” functions are those that are “sufficiently” differentiable, e.g., being twice continuously differentiable, three times differentiable, etc..) https://www.library.virginia.edu/news/2022/uva-walking-tour-enslaved-african-americans-at-uva<br /><br /> Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-63515087795450810632024-02-08T09:27:51.016-08:002024-02-08T09:27:51.016-08:00Hi Rhiannon, I am hoping for end of this year, but...Hi Rhiannon, I am hoping for end of this year, but it is likely to take a bit longer. If your daughter would like to beta read the text individually, email me at mathanthologyeditor on gmail.Sue VanHattumhttps://www.blogger.com/profile/10237941346154683902noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-16530956497474547412024-02-08T08:43:04.372-08:002024-02-08T08:43:04.372-08:00Sadly, we're away traveling during March and m...Sadly, we're away traveling during March and most of April, but really interested in your new books! I have a 12 year old daughter who used to love maths, but is currently burnt out and really hates anything traditional maths looking! When do you think these will be available? Best wishes, Rhiannon Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-73361876884599286072023-11-06T06:30:27.365-08:002023-11-06T06:30:27.365-08:00This is Sue. Google seems to be letting its blog t...This is Sue. Google seems to be letting its blog tools break. I cannot seem to sign in to post as myself. <br /><br />The whole internet is a bit unstable. Zoom recordings don't seem to be permanent. So I deleted that link. (My blog is full of old links that no longer work.)<br /><br />The algebra needed for Pythagorean triples is beyond most elementary students.<br /><br />The proofs of the Pythagorean theorem are not related to the triples. My favorites are mentioned in another post. (https://mathmamawrites.blogspot.com/2012/10/proving-pythagorean-theorem.html) Google has removed the pictures I included, but you might be able to make sense of it.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-18401514064618554202023-11-05T21:30:57.373-08:002023-11-05T21:30:57.373-08:00I just was reading your 'Online Math Circle: P...I just was reading your 'Online Math Circle: Pythagorean triples . the recording it says does not exist.I too am craving for discussions with passionate teachers . I do math enrichment for curious students in the elementary grades who enjoy doing math and was in particular interested in Pythagorean triples . So I wondered how do you introduce them and present them as an accessible mystery . How do we know what we know and how can students in the early grades like 1-4 make the first steps driven by their own natural creativity to get a first inkling about the problem of the Pythagorean theorem and its whole number solutions. Can we make the transition from the triples to find a general proof of the theorem by Pythagoras for any number or the length of the sides of the 3 squares of numbers children know in the grades 1-4 and not just the whole numbers. Thank you for your answer . Peter Koehler Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-10837072883045550612023-05-17T15:19:18.291-07:002023-05-17T15:19:18.291-07:00Is the time of death around 12:27pm or am I way of...Is the time of death around 12:27pm or am I way off? Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-7537934495877457512023-04-15T20:00:49.685-07:002023-04-15T20:00:49.685-07:00I'm glad you think so. Were you one of my read...I'm glad you think so. Were you one of my readers for an early version of the first book?Sue VanHattumhttps://www.blogger.com/profile/10237941346154683902noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-39553100303541773942023-03-13T01:18:41.318-07:002023-03-13T01:18:41.318-07:00Althea's Math Mysteries is so cool;)Althea's Math Mysteries is so cool;)<br />Aldierhttps://profi-akkusauger-test.de/akkusauger-aldi-sued-test/noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-7141839923096439322022-09-20T17:39:31.875-07:002022-09-20T17:39:31.875-07:00Thanks for commenting, Michelle. I've been inu...Thanks for commenting, Michelle. I've been inundated by spam comments lately, so it's really nice to get a real one!<br /><br />What grade level are you working with?<br />Sue VanHattumhttps://www.blogger.com/profile/10237941346154683902noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-62570829123988347002022-09-20T17:28:48.114-07:002022-09-20T17:28:48.114-07:00I push on my students to explain the "why&quo...I push on my students to explain the "why" whenever we work with an algorithm. With their help, I will often color code multiple algorithms showing the same problem. Once they see where the numbers are coming from, we push harder to explain why each algorithm works. Some, like the area model Sue showed, are very concrete. Usually when we do the traditional U.S. algorithm (the one on Sue's right) they explain that the zero shows that we are now multiplying 5 tens, not 5 ones so the product doesn't have any ones, it is 295 tens. Michellehttps://www.blogger.com/profile/09921244970889478836noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-4913405888267327382022-09-10T14:00:04.169-07:002022-09-10T14:00:04.169-07:00As you said, one thing Beast Academy is trying to ...As you said, one thing Beast Academy is trying to do is to give students a way to do math in their heads. And even more, they want to lay a foundation for students to understand the formula for factoring the difference of two squares.<br /><br />For parents, it's so hard to break out of the mindset we picked up in school. We learned that math is about getting answers quickly and efficiently and with as little thought as possible. If you're really good at math, you just look at the problem and know the answer right away, as if by magic.<br /><br />We weren't taught that not-knowing is perfectly fine, and that the struggle of figuring out how and why something works will pay dividends for years of future learning.Denise Gaskinshttps://denisegaskins.com/noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-32030443241205812822015-11-23T17:51:51.641-08:002015-11-23T17:51:51.641-08:00Here's another explanation of that last proof,...Here's another explanation of that last proof, with more detail: http://www.newyorker.com/tech/elements/einsteins-first-proof-pythagorean-theorem<br /><br />(Credited to Einstein!)Sue VanHattumhttps://www.blogger.com/profile/10237941346154683902noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-26326063617888137222015-11-23T14:40:30.746-08:002015-11-23T14:40:30.746-08:00Google messed up my old posts. If I can find the i...Google messed up my old posts. If I can find the images easily, I'll try to fix this within the next week. (If not, I may still try to fix many of the old posts over the holidays.)Sue VanHattumhttps://www.blogger.com/profile/10237941346154683902noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-42167230145323749082015-11-23T12:03:07.806-08:002015-11-23T12:03:07.806-08:00I can no see the activities, is there any app that...I can no see the activities, is there any app that I need to see them?MaNAtaliahttps://www.blogger.com/profile/04622006124196010069noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-21568043156620463052015-09-25T06:22:17.651-07:002015-09-25T06:22:17.651-07:00Monica, I don't do anything exciting with limi...Monica, I don't do anything exciting with limits - it's the other parts that I find exciting. I can't see your email. (I think you probably typed it in. But I don't get to see it.) Please email me at mathanthologyeditor@gmail.com for a copy of my stuff.Sue VanHattumhttps://www.blogger.com/profile/10237941346154683902noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-72183808475200152252015-09-22T01:11:59.863-07:002015-09-22T01:11:59.863-07:00Hi, I would like very much to know more about your...Hi, I would like very much to know more about your approach for teaching limits (I like your abstract, it woke up my interest). But I won't be able to come to the meeting. Would you please send me your materials? Thanks and enjoy the meeting. Monica Selvanoreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-83400734521286979592015-09-19T07:30:30.962-07:002015-09-19T07:30:30.962-07:00Yes, I'll share. In fact, I'm happy to sha...Yes, I'll share. In fact, I'm happy to share now. You can email me at mathanthologyeditor@gmail.com.<br /><br />The strand my proposed talk would be a part of is titled The Development and Adoption of Open Educational Resources for Teaching and Learning. Open Educational Resources (OER) are about sharing freely. There are two main ways people reserve some rights while still sharing freely, copyleft and creative commons.<br /><br />There are two meanings to the word free here. (Read more about copyleft and meanings of free here: http://www.gnu.org/gnu/thegnuproject.en.html) One is that you don't pay. Students will have to pay for a paper copy, but that will always be very affordable. And online copies are free that way. The other meaning of free is about freedom to make changes. Both meanings are important to me. I hate how much students pay for commercial textbooks. And I am so grateful to be able to use Matt Boelkins' and Dale Hoffman's materials in the way I want to. They each gave me modifiable files. I can mix topics up, rewrite sentences, and leave out exercises. I'm building my own materials from theirs.<br /><br />I think you've helped me clarify for myself how my talks fits the theme. Thanks for your comment and question. I hope to meet you at the meeting. ;^)Sue VanHattumhttps://www.blogger.com/profile/10237941346154683902noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-68737975330541797072015-09-19T05:34:39.914-07:002015-09-19T05:34:39.914-07:00I want to come to your session! And I want to see ...I want to come to your session! And I want to see your materials! Are you willing to share? Thanks! Jasminehttps://www.blogger.com/profile/14163491309269691356noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-31492773421540158582015-08-24T18:58:51.968-07:002015-08-24T18:58:51.968-07:00I value the whole discussion. I wish there was mor...I value the whole discussion. I wish there was more discussion of the modeling so that it didn't seem like our expert's numbers vs your expert's. Discussing the models would lend a lot more weight to the issue, plus raise the value of this kind of thinking.<br /><br />Here's the GeoGebra, if anyone wants to play: http://tube.geogebra.org/m/1509389<br /><br />Walt's reasoning looks solid to me.John Goldenhttps://www.blogger.com/profile/18212162438307044259noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-63460466309385238722015-08-23T16:34:48.682-07:002015-08-23T16:34:48.682-07:00Thank you for catching my error. That's two po...Thank you for catching my error. That's two posts in a row with silly errors. (Perhaps an indicator of my stress level, single parenting a 13-year-old.) <br /><br />Your answer is very close to John Golden's. I had thought the difference was because he integrated to look at continuous increase, but it's probably too big a difference for that to have made sense.<br /><br />I will work through the problem again myself. It's good I was vague when I posted on the blog where this was mentioned. 9% is still more than 3 times what the true increase is. So yeah, probably there probably very non-linear things happening. Unless that article included a typo.Sue VanHattumhttps://www.blogger.com/profile/10237941346154683902noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-13171398985309347832015-08-23T12:20:33.504-07:002015-08-23T12:20:33.504-07:00Sue, you did drop the 'H' from your second...Sue, you did drop the 'H' from your second sum 'S' - you can't subtract the 16.6 and the 6.6 because they are in different "units".<br /><br />The proper equation is (sum if we reduce now) = (sum if we reduce after 5 years) + (sum of emissions over the next 5 years). Using N for current emissions rate and H for emissions in 5 years, this is <br />(N * 16.58) = (N * r^5 * 6.66) + (N * (r^5-1)/(r-1))<br />Solving this numerically for r I get a value of about 1.096, or an assumed 9.6% per year increase.<br /><br />Notes: I used 16.58 instead of 16.66 because (.94)^85 is still about ~.005, so it is more accurate. I used five years of increase instead of the six in your equation, thus H = N * r^5 and the 5-year sum is N * (r^5-1)/(r-1).<br /><br />While solving numerically by hand (Newton-Raphson) I noticed that the second derivative was large, so the exact solution may be very sensitive to the inputs - i.e. if the 15% was rounded from 14.5, or the 6% was really 6.2% you might get a full percent or more difference in the answer.<br /><br />I also note that the final term in each sum is the assumed emissions in the year 2100. The fact that they are so small brings the feasibility of a continuous decrease into question. For 6% reduction, the final term is about 1/200 of current emissions, whereas for 15% reduction it is barely more than a factor of 500,000 below 2020 emissions (which are 58% higher than current using 9.6% growth). These levels would represent a wholesale shift away from carbon emitting, rather than settling at a new, reduced, stable level.<br /><br />I suspect that the 6% and 15% numbers come not from a calculation of total carbon emitted into the air, but the results of a more complex model that represents how the atmosphere responds to total airborne carbon, and that such a model would be very non-linear - therefore the increase in needed reduction may not correspond to achieving a fixed value of the integral at all.Walthttps://www.blogger.com/profile/05235362518037728416noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-30002198474520789662015-08-22T10:52:10.306-07:002015-08-22T10:52:10.306-07:00They are row equivalent, but they are not the same...They are row equivalent, but they are not the same. I mistakenly thought they were in reduced echelon form. Silly me.Sue VanHattumhttps://www.blogger.com/profile/10237941346154683902noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-4240654867991319912015-08-22T10:39:42.197-07:002015-08-22T10:39:42.197-07:00Oh! So, in an augmented matrix (last column repres...Oh! So, in an augmented matrix (last column represents the constant on the right side of the =), I still need to finish up, and I'll get 0 1 on the last column of both of these. Duh. (Since we always stop as soon as we know a system is inconsistent, I hadn't thought about including the last column in my process.)<br /><br />I was going to post in math stack exchange. Thank goodness I didn't. Feeling silly...<br /><br />So now my question becomes whether we can consider the three cases (one, many, or no solutions), and build a simpler proof than Lay's. I'll keep thinking about that.Sue VanHattumhttps://www.blogger.com/profile/10237941346154683902noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-43972713028721644252015-08-22T10:30:12.054-07:002015-08-22T10:30:12.054-07:00Are those matrices not row equivalent to each othe...Are those matrices not row equivalent to each other? You can multiply the second row by any arbitrary value (so 0, 0, -3 can be changed into 0, 0, 2.5) and you can then add that to the first row to change the 3rd column value to any arbitrary value.Haohttps://www.blogger.com/profile/02348974241652264510noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-7773583358412999312015-08-22T10:19:00.284-07:002015-08-22T10:19:00.284-07:00You've got that right, John.You've got that right, John. Sue VanHattumhttps://www.blogger.com/profile/10237941346154683902noreply@blogger.com