@USDescartes

Math problems and occasional bad-stats rants. Husband & Father; Math Teacher At Large; Experimental Physicist; Book Editor; HMC BS; OSU PhD; Both in Physics

 Columbus, OH
nandor.org/mj
Joined January 2009
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#POTD #Math #Geometry #Advanced Problem of the Day! This is possibly on the more difficult side, but this one came to me as I was falling asleep last night, so I thought I'd write it up. Enjoy! And don't forget to explain your reasoning!
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Problem of the Day! Another in my list of 2026 questions. Find the exact answer. #POTD #Math #Integration #Floor #Ceiling
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Nice job, folks. Here's how I chose to look at it (not completely dissimilar to others' work):
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Problem of the Day! A little tetration problem for you.... #POTD #Math #Tetration
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Huh. Just noticed that today is a Pythagorean triple (10/24/26). I got curious, and there are only a handful (22) each century, and today is the last one of the 21st century. Assuming order doesn't matter, then here are all of them (using Americanized date forms): #PythagoreanTriples #Pythagorean #Triples
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Problem of the Day! Part B is a doozy. In fact, I'm not sure how to answer it correctly myself, after a couple hours of trying. I mean, I HAVE answers... but even after years of working with Complex numbers and exponents, I'm not sure how to check if I'm correct! #POTD #Math #Logarithms #Exponentials #Difficult
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Now here's my issue with the existence of complex answers, beyond simply 𝜓^ln(2/5). That is, I'm not sure the two FAMILIES of answers are valid or not.
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Obviously, Mathematica is not the final arbiter of mathematical truth, but I DO find it puzzling... and, of course, as with all things having to do with Complex numbers, the rules regarding exponents are different between Complex and Real numbers.
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As of 5:21pm PDT today, it has been EXACTLY 36 years since I told my (now) wife that I loved her! Our first date was 36 years, 1 month, and 9 days ago, so it took me over a month to say it. But get this: some time in the next week or so will be the 36th anniversary of our first kiss! Yes, we took things EXTREMELY slowly. 😍 👩‍❤️‍👨 🩷🥰
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Problem of the Day! Here's an equation with x's all over the place. #POTD #Math #Algebra #Advanced
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Problem of the Day! Today's my travel (back home) day, and I usually don't travel well so we'll see about the next few days. However, here's a nice "2026" integral! #POTD #Math #Calculus #Integration #Medium
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Here's the lemma.
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Oops. I forgot to mention that @Ionely_warrior solved it with CA, as well!
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Problem of the Day! Straightforward algebra this time. #POTD #Math #Algebra
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Some solid solutions are below. Here's how *I* did it:
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Problem of the Day! I thought about this easy-but-interesting problem on the plane yesterday. Here's another 2026 question: on a 24-hour clock, what is the angle (degrees or radians) between the hands on a 24-hour clock (seen below) at the time 8:26pm? #POTD #Math #Geometry #Easy #Tricky
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@DjlocktiteX and @_Manuel_Ruiz_ have excellent solutions, and there is not much more to be said. I guess we could point out that I did not specify "what is the smaller angle between the hands," so both answers (150.5° and 209.5°) are correct! Also note that clocks are BUILT to be measured by degrees and not radians (60 seconds per minute, 60 minutes per hour, 12 (or 24) hours for both hands to make a complete circuit), so in THIS case, degrees are the "natural units" of measurement.
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Also, as (sort of) seen in the picture, did you know that pictures of (regular) clocks almost always pictures of clocks almost always read approximately 10:10, because it looks like a smile (supposedly)? Of course, in this picture would be 8:10pm.
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