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Aunt Dora Baggins
Immortal
Mar 15 2007, 9:23pm
Post #1 of 15
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It doesn't happen very often,
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but sometimes my math books have problems in them that really make me laugh. Here's one I found while preparing tomorrow's lecture:
(Referring to the limaçon r = 1 + sin q) From Figure 18 it appears that the limaçon loses its dimple when c = 1/2. Prove this.
(James Stewart Calculus 5th ed. section 11.3 problem 53b)
Here's one that's made me laugh for the past 20 years:
Consider the set whose only element is the moon. Is this set a vector space under the operations moon + moon = moon and k(moon) = moon for every real number k? Explain your reasoning.
(Howard Anton Elementary Linear Algebra 9th ed. section 5.1 problem 27)
A couple of word problems:
Billy Joe McCallister jumped off the Tallahatchie Bridge, 70 ft above the water, with a bungee cord tied to his legs. If he was 6 ft above the water 2 sec after jumping, when what was the average rate of change of his altitude as the time varied form 0 to 2 sec?
(Mark Dugopolski College Algebra 3rd ed. section 2.1 problem 72)
And then there's this one, also from the Dugopolski book:
The wizard Gandalf is creating a massive crystal ball. To acheive maximum power, the orb must be a perfect solid sphere of clear crystal mounted on a square solid silver base, as shown in the figure. The wizard has determined that the diameter of the sphere must equal the length of the side of hte square base, and the thickness of the base must be p in. Find the exact radius of the sphere if the toatal amount of material used in the sphere and base must be 1296 p cubic inches. If it turns out that the sphere is not powerful enough, Gandalf plans to make the sphere and base of solid dilitheum crystal. For this project the diameter of the sphere must be 2 in. less than the length of the side of the base and the thickness of the base must be 2 in. Find the approximate radius of the sphere if the total volume of material used in the sphere and base must be 5000 cubic inches.
(Mark Dugopolski College Algebra 3rd ed. section 3.4 problem "linking concepts.")
Dugopolski put a lot of effort into being entertaining, but my students didn't always appreciate it.
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"For DORA BAGGINS in memory of a LONG correspondence, with love from Bilbo; on a large wastebasket. Dora was Drogo's sister, and the eldest surviving female relative of Bilbo and Frodo; she was ninety-nine, and had written reams of good advice for more than half a century."
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Chance Meeting at Rivendell: a Tolkien Fanfic
and some other stuff I wrote...
leleni at hotmail dot com
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Draupne
Forum Admin
/ Moderator
Mar 15 2007, 10:01pm
Post #2 of 15
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If you have one moon and add it to itself
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wouldn't you have to have Gandalf make an extra one in dilitheum crystal first?
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Menelwyn
Rohan
Mar 15 2007, 10:04pm
Post #3 of 15
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Here are a couple that I've always remembered
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both from Eugene Hecht's Optics, 2nd ed.
problem 5.5: "Locate the image of an object placed 1.2 m from the vertex of a gypsy's crystal ball, which has a 20-cm diameter (n = 1.5). Make a sketch of the thing (not the gypsy, the rays)."
problem 5.43: "You are herewith requested to design a little dentist's mirror to be fixed at the end of a shaft for use in the mouth of some happy soul. The requirements are (1) that the image be erect as seen by the dentist and (2) that when held 1.5 cm from a tooth the mirror produces an image twice life-size."
There was also one from my final in my optics course (the same course with the above textbook, but not from that book) that began something like "A physics students goes to the beach. Of course she takes along her polarizing sunglasses and her light intensity meter." Of course she brought them.
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Aunt Dora Baggins
Immortal
Mar 15 2007, 10:05pm
Post #4 of 15
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I think that must be the correct answer.
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wouldn't you have to have Gandalf make an extra one in dilitheum crystal first?
(I know what Anton was getting at. The moon is the zero vector. But for some reason it's funnier calling it the moon. For some reason "the moon" is a funny phrase, at least to me. "The cow jumped over the moon" is a lot funnier than "The cow jumped over the sun" would be.)
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"For DORA BAGGINS in memory of a LONG correspondence, with love from Bilbo; on a large wastebasket. Dora was Drogo's sister, and the eldest surviving female relative of Bilbo and Frodo; she was ninety-nine, and had written reams of good advice for more than half a century."
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Chance Meeting at Rivendell: a Tolkien Fanfic
and some other stuff I wrote...
leleni at hotmail dot com
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GaladrielTX
Tol Eressea
Mar 15 2007, 11:06pm
Post #6 of 15
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~~~~~~~~
I used to be GaladrielTX, but I lost my TX and an hour over the weekend. Stupid Daylight Saving Time!
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Draupne
Forum Admin
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Mar 15 2007, 11:27pm
Post #7 of 15
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But if the moon is a zero vector
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jumping over it shouldn't be a problem.
Not sure about jumping over a crystal sphere though. Spheres are OK as long as you're in the far-field, but by jumping it you might end up in its near-field and then things get complicated and dispersive and you'd disintegrate into different wave-lengths.
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Draupne
Forum Admin
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Mar 15 2007, 11:32pm
Post #8 of 15
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I'm quite schocked that she actually has time to go to the beach when she should be at home learning :-)
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Aunt Dora Baggins
Immortal
Mar 16 2007, 9:18am
Post #9 of 15
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My brother recalls taking a math test once in which a problem began:
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"Brad and Janet are driving past a castle..."
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"For DORA BAGGINS in memory of a LONG correspondence, with love from Bilbo; on a large wastebasket. Dora was Drogo's sister, and the eldest surviving female relative of Bilbo and Frodo; she was ninety-nine, and had written reams of good advice for more than half a century."
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Chance Meeting at Rivendell: a Tolkien Fanfic
and some other stuff I wrote...
leleni at hotmail dot com
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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grammaboodawg
Immortal
Mar 16 2007, 9:30am
Post #10 of 15
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I almost didn't respond simply because the work "math" was here
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but I'm glad I braved the swamps of Emyn Math to read these. THAT'S SO COOL!
The geeks are infiltrating school books. That's awesome!!! :D
 
Trust him... The Hobbit is coming!
"Barney Snow was here." ~Hug like a hobbit!~ "In my heaven..."
TORn's Observations Lists
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dernwyn
Forum Admin
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Mar 16 2007, 4:12pm
Post #11 of 15
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*chuckle*! But what's scary is
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I almost understand what's going on in those questions...
I'll offer a simpler one - one that's actually from one of my hubby's 7-th grade math textbooks. I don't recall the exact numbers, but it was something like: "Farmer Brown had 5 and 7/8 haystacks in one field and 17 and 3/10 haystacks in another. If he combines them all, how many haystacks will he have?"
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"Confusticate and bebother these dwarves!"
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Advising Elf
Rohan
Mar 16 2007, 4:45pm
Post #12 of 15
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Yahoo!Group with good stuff to download:
http://groups.yahoo.com/group/LOTRgoodies/
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Aunt Dora Baggins
Immortal
Mar 16 2007, 5:03pm
Post #13 of 15
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Highlight to see my spoiler answer:One!
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"For DORA BAGGINS in memory of a LONG correspondence, with love from Bilbo; on a large wastebasket. Dora was Drogo's sister, and the eldest surviving female relative of Bilbo and Frodo; she was ninety-nine, and had written reams of good advice for more than half a century."
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Chance Meeting at Rivendell: a Tolkien Fanfic
and some other stuff I wrote...
leleni at hotmail dot com
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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silneldor
Half-elven
Mar 17 2007, 4:14pm
Post #14 of 15
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Who's doing the mooning? How big is it? Is it moving?
Heavens! Hector's vector! Somebody get the rector!
"Tolkien, like Lewis, believed that, through story, the real world would become a more magical place, full of meaning. We see its patterns and colors in a fresh way. The recovery of a true view of the world applies both to individual things, like hills and stones, and to the cosmic - the depths of space and time itself. For in sub-creation, in Tolkien's view, there is a "survey" of space and time. Reality is captured on a miniature scale. Through stories like The Lord of the Rings, a renewed view of things is given, illuminating the homely, the spiritial, the physical, and the moral dimensions of the world."
Tolkien and C.S. Lewis- The Gift of Friendship -Duriez
The magnificent beech
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Aunt Dora Baggins
Immortal
Mar 17 2007, 6:24pm
Post #15 of 15
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Years ago I posted that last question (about Gandalf)
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and some pedantic person here sniffed that everyone knows it isn't Gandalf who makes the palantir, it's Feanor! Nice to know the people here are more geeky than the author of my algebra book. :-)
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"For DORA BAGGINS in memory of a LONG correspondence, with love from Bilbo; on a large wastebasket. Dora was Drogo's sister, and the eldest surviving female relative of Bilbo and Frodo; she was ninety-nine, and had written reams of good advice for more than half a century."
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Chance Meeting at Rivendell: a Tolkien Fanfic
and some other stuff I wrote...
leleni at hotmail dot com
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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