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ith what i have though mark anderson s andertoons for the 12th of may i would have sworn was a repeat if it is i don t seem to have featured it before it gives us wavehead i ve learned his name is not consistent learning about division the first kind of division at least with a quotient and a remainder the novel thing here with integer division is that the result is not a single number but rather an ordered pair i hadn t thought about it that way before i suppose since integer division and ordered pairs are introduced so far apart in one s education mark anderson s andertoons for the 12th of may 2022 this and the great many other essays mentioning andertoons are at this link this includes my discoveries about wavehead s true name we mostly put away this division with remainders as soon as we get comfortable with decimals 19 div 4 becoming 4 remainder 3 or 4 75 or 4 latex frac 3 4 all impose a roughly equal cognitive load but this division reappears in high school algebra when we start dividing polynomials almost anything you can do with integers there s a similar thing you can do with polynomials this is not just because you can rewrite the integer 4 as the polynomial f x 0x 4 there may be something easier to understand in turning into remainder a thing happening here is that integer arithmetic is a ring we study a lot of rings as it s not hard to come up with things that look like addition and subtraction and multiplication rings we don t assume to have division that stays in your set they can turn into pairs like with integers or with polynomials having that division makes the ring into a field so called because we don t have enough things called a field already scott hilburn s the argyle sweater for the 16th of may 2022 this and the not quite as many essays bringing up the argyle sweater are at this link scott hilburn s the argyle sweater for the 16th of may is one of the prime number strips from this collection about the only note worth mention is that the indivisibility of 3 depends on supposing we mean the integer 3 if we decided 3 was a real number we would have every real number other than zero as a divisor there s similar results for complex numbers or polynomials i imagine there s a good fight one could get going about whether 3 in integer arithmetic is the same number as 3 in real arithmetic i m not ready for that right now though i like the blood bag dracula s drinking from nice touch dave coverly s speed bump for the 16th of may 2022 this and fewer essays than i would have thought about some topic raised by speed bump are at this link i would have thought dave coverly almost as good to me as scott hilburn was dave coverly s speed bump for the 16th of may names the ways to classify triangles based on common side lengths or common angles there is some non absurdity in the joke s premise not the existence of these particular pennants but that someone who loves a subject enough to major in it will often be a bit fannish about it yes it s difficult to imagine going any other way you need to get to a pretty high leve of mathematics to go seriously into triangles but the option is there dave whamond s reality check for the 3rd of june is the other comic strip playing on the definition of prime here it s applied to the hassle of package delivery and the often comical way that items will get boxed in what seems to be no logical pattern but there is a reason behind that lack of pattern it is an extremely hard problem to get bunches of things together at once it gets even harder when those things have to come from many different sources and get warehoused in many disparate locations add to that the shipper s understandable desire to keep stuff sitting around waiting for as little time as possible so the waste in package and handling and delivery costs seems worth it to send an order in ten boxes than in finding how to send it all in one dave whamond s reality check for the 3rd of june 2022 this and the quite a few other essays bringing up reality check are at this link dave whamond now that s someone almost as prolific for my purposes as scott hilburn is plus he puts in that marginalia joke for the squirrel most days it feels like an obvious offense to reason to use four boxes to send five items it can be hard to tell whether the cost of organizing things into fewer boxes outweighs the additional cost of transporting mostly air this is not to say that i think the choice is necessarily made correctly i don t trust organizations to not decide i dunno we always did it this way i want instead to note that when you think hard about a question it often becomes harder to say what a good answer would be i can give you a good answer though if your question is how to read more comic strips alongside me i try to put all my reading the comics posts at this link you can see something like a decade s worth of my finding things to write about students not answering word problems thank you for reading along with this kindly share this email a link to a friend opens in new window email print opens in new window print share on x opens in new window x more share on facebook opens in new window facebook share on linkedin opens in new window linkedin share on pinterest opens in new window pinterest share on reddit opens in new window reddit share on telegram opens in new window telegram share on tumblr opens in new window tumblr share on whatsapp opens in new window whatsapp like loading author joseph nebus posted on wednesday 8 june 2022 wednesday 8 june 2022 categories comic strips math mathematics maths tags andertoons reality check speed bump the argyle sweater 3 comments on reading the comics june 3 2022 prime choices edition how may 2022 treated my mathematics blog the easy way to put this article is if i don t read my mathematics blog why should anyone else there is truth to this i have mentioned several times that this has been a difficult year for me and i ve had to ration where i put my energy i ve avoided going a whole week without a post but it s only by reposting old material that i ve managed that even the old standby of writing about the mathematics in comic strips has fallen short as comic strip master command isn t sending so many worth my attention these days these are strange times the result is a decline in my readership although it s less of one than i had expected there were no comments at all around here in may which have to say seems fair there wasn t much to comment on especially with just four essays posted that s my lowest posting volume in years it s also not the first time i had zero comments in a month which takes some sting off yes i see how wordpress claims i have 997 followers you can join that group by using the follow nebusresearch button at the upper right of the screen i suspect a lot of them aren t following closely though so there were 2 057 page views here in may that s a bit below the twelve month running mean of 2 212 3 views per month leading up to may and below the running median of 2 114 5 views per posting the number looks impressive though with 514 3 page views per posting that beats the running mean of 309 1 and median of 302 8 there were 1 358 unique visitors recorded in may that s again a slight decline from the 1 528 2 running mean and 1 461 5 running median and again per posting the numbers seem impressive 339 5 unique visitors with each posting above the mean of 213 2 and median of 211 3 the implication yes is if i didn t post at all i d have infinitely many readers a conclusion which hurts my feelings there were twenty likes given in may up from april but still below the mean of 35 3 and median of 33 it s a per posting average of 5 0 likes per posting above the mean of 4 6 and median of 4 2 but there s no way there s statistical significance to that and of course no comments compared to a running mean of 9 7 and median of 7 with so few essays posted it s easy to report the order of their popularity i m not sure whether their order depends on how interesting the text was or how early in the month they were posted there s no way the difference is statistically significant but here s the may 2022 pieces ranked most popular to least reading the comics may 7 2022 does comic strip master command not do mathematics anymore edition how april 2022 treated my mathematics blog something neat about triangles again about chances of winning on the price is right again wordpress figures i started the month with a grand total of 1 714 posts these all together drew 3 319 comments and 161 316 page views from 97 265 recorded unique visitors it also figures my average post for the month had 876 words in it bringing my average post for the year 2022 down to 1 037 words per posting i ve managed to put together 40 451 words so far this year this surprises me by being close to half what i ve managed on my humor blog where i post every day there i have several regular columns such as story comic plot summaries that are popular and relatively easy to write having said all that will this look at may s figures affect my writing any i do think i have enough comic strips for a post that should be next wednesday at least if comic strip master command works with me there could be more but this all will depend on my emotional and energy reserves some of my faithful readers may wonder am i preparing to say something sad about this year s a to z i m not prepared to say not yet what i am is thinking about whether i want to commit to such a big hard project i am aware how much it would tax me to do and while i would like to have it done there is so much doing to get there it will depend on how june treats me kindly share this email a link to a friend opens in new window email print opens in new window print share on x opens in new window x more share on facebook opens in new window facebook share on linkedin opens in new window linkedin share on pinterest opens in new window pinterest share on reddit opens in new window reddit share on telegram opens in new window telegram share on tumblr opens in new window tumblr share on whatsapp opens in new window whatsapp like loading author joseph nebus posted on wednesday 1 june 2022 wednesday 8 june 2022 categories math mathematics maths meta tags 2022 may popularity readership wordpress 1 comment on how may 2022 treated my mathematics blog about chances of winning on the price is right again while i continue to wait for time and muse and energy and inspiration to write fresh material let me share another old piece this bit from a decade ago examines statistical quirks in the price is right game shows offer a lot of material for probability questions the specific numbers have changed since this was posted but the substance hasn t i got a bunch of essays out of one odd incident mentioned once on the show and let me do something useful with that now to the serious game show fans yes i am aware that the item up for bid is properly called the one bid i am writing for a popular audience the name one bid comes from the original 1950s run of the show when the game was entirely about bidding for prizes a prize might have several rounds of bidding or might have just the one and that format is the one used for the item up for bid for the current 1972 present show putting together links to all my essays about trapezoid areas made me realize i also had a string of articles examining that problem of the price is right with drew carey s claim that only once in the show s history had all six contestants winning the item up for bids come from the same seat in contestants row as with the trapezoid pieces they form a more or less coherent whole so let me make it easy for people searching the web for the likelihood of clean sweeps or of perfect games on the price is right to find my thoughts continue reading about chances of winning on the price is right again kindly share this email a link to a friend opens in new window email print opens in new window print share on x opens in new window x more share on facebook opens in new window facebook share on linkedin opens in new window linkedin share on pinterest opens in new window pinterest share on reddit opens in new window reddit share on telegram opens in new window telegram share on tumblr opens in new window tumblr share on whatsapp opens in new window whatsapp like loading author joseph nebus posted on wednesday 25 may 2022 wednesday 25 may 2022 categories math mathematics maths probability recreational mathematics tags drew carey game shows matlab octave probability the price is right tv 1 comment on about chances of winning on the price is right again something neat about triangles again i apologize for not having anything fresh to share today it s been a difficult week one of many so i would like to share something from years ago and something i still find delightful i was reading a biography of donald coxeter one of the most important geometers of the 20th century and it mentioned in passing something coxeter referred to as morley s miracle theorem the theorem was proved in 1899 by frank morley who taught at haverford college if that sounds vaguely familiar that s because you remember it s where dave barry went and then johns hopkins which may be familiar on the strength of its lacrosse team and published this in the first issue of the transactions of the american mathematical society and yes perhaps it isn t actually important but the result is so unexpected and surprising that i wanted to share it with you the biography also includes a proof coxeter wrote for the theorem one that s admirably straightforward but let me show the result without the proof so you can wonder about it first start by drawing a triangle it doesn t have to have any particular interesting properties other than existing i ve drawn an example one the next step is to cut into three equal pieces each of the interior angles of the triangle and draw those lines i m doing that in separate diagrams for each of the triangle s three original angles because i want to better suggest the process i should point out this trisection of the angles can be done however you like which is probably going to be by measuring the angles with a protractor and dividing the angle by three i made these diagrams just by sketching them out so they aren t perfect in their measure but if you were doing the diagram yourself on a sheet of scratch paper you wouldn t bother getting the protractor out either and famously you can t trisect an angle if you re using just compass and straightedge to draw things but you don t have to restrict yourself to compass and straightedge for this now the next bit is to take the points where adjacent angle trisectors intersect that is for example where the lower red line crosses the lower green line where the upper red line crosses the left blue line and where the right blue line crosses the upper green line draw lines connecting these points together and this...
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