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Posts

April 20, 2014

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1:20 AM | Generalizing an already tough integral
I did the case $p=1$ here. The generalization to higher $p$ may involve higher-order derivatives as follows: $$\begin{align}K_p &= \int_0^{\pi/2} dx \frac{x^{2 p}}{1+\cos^2{x}} = \frac1{2^{4 p-1}} \int_{-\pi}^{\pi} dy \frac{y^{2 p}}{3+\cos{y}} \end{align}$$ So define, as before, $$J(a) = \int_{-\pi}^{\pi} dy \frac{e^{i a y}}{3+\cos{y}} $$ Then $$K_p = \frac{(-1)^p}{2^{4 p-1}} \left [\frac{d^{2 p}}{da^{2 p}} J(a) \right ]_{a=0}$$ […]

April 19, 2014

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7:46 PM | cherry-merchant: Sierpinski transformation
cherry-merchant: Sierpinski transformation
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4:14 PM | mathani: Get you best paper, cut a circle and fold it so that...
mathani: Get you best paper, cut a circle and fold it so that the circumference falls on a fixed point inside. Repeat, using random folds. Now see the creases. This is how you paper-fold an ellipse.
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12:30 PM | 4/19/14
4 - 1 = √9 * 1^4 Also: 4 - 1 = √9 = |1 - 4| Also: 4! = 19 + 1 + 4 Also: 41914 is a palindrome
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2:13 AM | centerofmath: The Ulam spiral shows a pattern in the...
centerofmath: The Ulam spiral shows a pattern in the (unpredictable) primes

April 18, 2014

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8:01 PM | A Limerick!
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4:33 PM | Salvador Dalí, Crucifixion (Corpus Hypercubus), 1954
Salvador Dalí, Crucifixion (Corpus Hypercubus), 1954
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2:13 PM | Administration
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2:04 PM | centerofmath: The Ulam spiral shows a pattern in the...
centerofmath: The Ulam spiral shows a pattern in the (unpredictable) primes
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1:25 PM | The Four-Color Theorem
BIRTHDAY CHALLENGE: Pick a line drawing of the Map of Nigeria (like the one below) with the borders of its states included and try to color each state with one […]
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12:30 PM | 4/18/14
√4 = 1 * 8 * 1 / 4 Also: 4 = 18 - 14 Also: |4 + 1 - 8| = |1 - 4| Also: 41814 is a palindrome
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12:18 PM | Good Friday
(Click on the cartoon to see the full image.) (C)Copyright 2014, C. Burke.Or possibly labeled "Passion, Death, Resurrection"? Good Friday is part of the Paschal Triduum, which can also be spelled "Pascal", but I wanted to avoid confusion and basically hang a lampshade on it.
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11:30 AM | Big Helping of Friday Potpourri
ICYM them, quite a mishmash of varied links from the past week (something for everyone perhaps): 1) Martin Gardner's more philosophical writings here: http://martin-gardner.org/Philosophy.html 2) Who knew there was so much to know about the arrangement of dice? Tanya Khovanova filled us in on what she learned from John Conway: http://blog.tanyakhovanova.com/?p=489 3) Just in case you've been
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7:20 AM | Επαναληπτικές ασκήσεις για τα μαθηματικά κατεύθυνσης Γ Λυκείου από τον Γ.Μαυρίδη
  Επιλεγμένες ασκήσεις (με τις λύσεις τους) για την τελική επανάληψη σας,από τον φίλο και συνάδελφο Γιώργο Μαυρίδη. Οι ασκήσεις προέρχονται από την ανανεωμένη έκδοση του βοηθήματος της Γ Λυκείου που ξεχωρίζει  για τα πολλά λυμένα θέματα που περιέχει , την εύληπτη και […]
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6:44 AM | Objectifying
No summary available for this post.
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3:08 AM | Real graphs have curves
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2:43 AM | mathani: Get you best paper, cut a circle and fold it, fold it...
mathani: Get you best paper, cut a circle and fold it, fold it so that the circumference falls on a fixed point inside. Repeat, using random folds. Now see the creases. This is how you paper-fold an ellipse.

April 17, 2014

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6:55 PM | "If Tomorrow Starts Without Me"
My cousin Patricia (she'll always be "Patty" to me) read the following poem at her mother's funeral yesterday. (That would be my Aunt Pat.) There wasn't a dry eye in the place. And if that didn't get you, then her sister Debbie, in her eulogy, remembering those who have left us since last August did: my Mom, their sister Barbara, my niece Lisa and most recently, our cousin Mary Ann. To that, I'll add a few more: my Uncle Eddie (on the other side of the family) last week, my colleague Ms. […]
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2:58 PM | Bring Radicals
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12:30 PM | 4/17/14
4 = (1 + 7) - (1 * 4) Also: 4 * 1 = 7 - (1 * 4) Also: 41714 is a palindrome
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11:15 AM | Thursday Meditation From Mathodist Pastor Keith Devlin ;-)
Just a mathematical meditation for today...:About 10 days ago in a longish post over at MathTango I included some links to Keith Devlin materials -- one of my favorites was a podcast he did for NPR's "On Being," an always-wonderful radio-hour.  In that conversation he made the following observation, which I fancy, regarding a transition on the road to becoming a mathematician [bold added]:"...that's when I became a mathematician; that's what I stumbled on at age 15 or 16 when here I was […]

April 16, 2014

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11:37 PM | Photo
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11:19 PM | Test problem
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8:26 PM | Photo
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7:57 PM | Calculus 2
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7:55 PM | @pickover: Not only does 12+1=11+2, but the letters “twelve plus one” rearrange to give you “eleven...
@pickover: Not only does 12+1=11+2, but the letters “twelve plus one” rearrange to give you “eleven...
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4:00 PM | The New Math Teacher
Have you met our new colleague? He's a teletubby whose stomach plays Khan Academy videos. Continue reading →
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1:30 PM | Math Limericks
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1:09 PM | Pirates
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1:06 PM | Funny How Things Work Out
It had been my intention, if I could muster the discipline and determination, to have a new comic each day this week because I'm off. Funny how things work out. It seems like every day is booked with something, the first three days being the worst. Sure, I might have something by Thursday, but that's hardly "every day" of the week. That's catch-up time. There will be an update, and if I can spend Friday working on things, I'll plan out next week ahead of time. I hope. And next Monday and […]
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