[math-fun] Mixed numbers?
A young friend has to convert all his "improper" fractions to mixed numbers. When he repeated my remark that mathematicians, scientists, and engineers shun mixed numbers, he got hauled up before the dean, who angrily insisted that mathematicians actually prefer mixed numbers. Does anybody know a computer algebra system that even offers mixed numbers as an output format? An input format?? --rwg A still younger friend emailed: What?? 3½=3+½?? That's crazy! I was showing this guy rotation matrices, and he seriously asked, "What's a degree? Is that like pi/180?" --rwg
Seems like this could be a learning opportunity for the dean. Could someone scrape up a minyan of mathematicians from the local uni to pay him a visit? On Thu, Dec 10, 2015 at 6:50 AM, Bill Gosper <billgosper@gmail.com> wrote:
A young friend has to convert all his "improper" fractions to mixed numbers. When he repeated my remark that mathematicians, scientists, and engineers shun mixed numbers, he got hauled up before the dean, who angrily insisted that mathematicians actually prefer mixed numbers. Does anybody know a computer algebra system that even offers mixed numbers as an output format? An input format?? --rwg A still younger friend emailed:
What?? 3½=3+½?? That's crazy!
I was showing this guy rotation matrices, and he seriously asked, "What's a degree? Is that like pi/180?" --rwg _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
If this school is in the Boston area, I'll be the second in Allan's minyan. Though what we're trying to do is more like separating a person (the dean) from a demon that's inhabiting him (the dean's erroneous belief) than reciting kaddish for someone who's died. Is there a standard term in Catholicism for a posse of exorcists? Jim On Thu, Dec 10, 2015 at 8:18 AM, Allan Wechsler <acwacw@gmail.com> wrote:
Seems like this could be a learning opportunity for the dean. Could someone scrape up a minyan of mathematicians from the local uni to pay him a visit?
On Thu, Dec 10, 2015 at 6:50 AM, Bill Gosper <billgosper@gmail.com> wrote:
A young friend has to convert all his "improper" fractions to mixed numbers. When he repeated my remark that mathematicians, scientists, and engineers shun mixed numbers, he got hauled up before the dean, who angrily insisted that mathematicians actually prefer mixed numbers. Does anybody know a computer algebra system that even offers mixed numbers as an output format? An input format?? --rwg A still younger friend emailed:
What?? 3½=3+½?? That's crazy!
I was showing this guy rotation matrices, and he seriously asked, "What's a degree? Is that like pi/180?" --rwg _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
mixed numbers are not even recognized by students or the general public in many european countries. adam atkinson has collected data worldwide on this question. not sure if he's a funster On Thursday, December 10, 2015, Bill Gosper <billgosper@gmail.com> wrote:
A young friend has to convert all his "improper" fractions to mixed numbers. When he repeated my remark that mathematicians, scientists, and engineers shun mixed numbers, he got hauled up before the dean, who angrily insisted that mathematicians actually prefer mixed numbers. Does anybody know a computer algebra system that even offers mixed numbers as an output format? An input format?? --rwg A still younger friend emailed:
What?? 3½=3+½?? That's crazy!
I was showing this guy rotation matrices, and he seriously asked, "What's a degree? Is that like pi/180?" --rwg _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com <javascript:;> https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- Thane Plambeck tplambeck@gmail.com http://counterwave.com/
At least in grade school, I was likewise required to convert fractions to mixed form. I agree that automatically doing this (and calling the raw ratio "improper") is pretty silly. Still, if you need to know the size of a number you will care about knowing at least approximately the integer part. So it's not just unadulterated nonsense. —Dan
On Dec 10, 2015, at 3:50 AM, Bill Gosper <billgosper@gmail.com> wrote:
A young friend has to convert all his "improper" fractions to mixed numbers. When he repeated my remark that mathematicians, scientists, and engineers shun mixed numbers, he got hauled up before the dean, who angrily insisted that mathematicians actually prefer mixed numbers. Does anybody know a computer algebra system that even offers mixed numbers as an output format? An input format?? --rwg A still younger friend emailed:
What?? 3½=3+½?? That's crazy!
I was showing this guy rotation matrices, and he seriously asked, "What's a degree? Is that like pi/180?" --rwg
I think the only good thing about improper fractions is that they're an intermediate stage in continued fractions. On Thu, Dec 10, 2015 at 7:37 AM, Dan Asimov <dasimov@earthlink.net> wrote:
At least in grade school, I was likewise required to convert fractions to mixed form. I agree that automatically doing this (and calling the raw ratio "improper") is pretty silly.
Still, if you need to know the size of a number you will care about knowing at least approximately the integer part. So it's not just unadulterated nonsense.
—Dan
On Dec 10, 2015, at 3:50 AM, Bill Gosper <billgosper@gmail.com> wrote:
A young friend has to convert all his "improper" fractions to mixed numbers. When he repeated my remark that mathematicians, scientists, and engineers shun mixed numbers, he got hauled up before the dean, who angrily insisted that mathematicians actually prefer mixed numbers. Does anybody know a computer algebra system that even offers mixed numbers as an output format? An input format?? --rwg A still younger friend emailed:
What?? 3½=3+½?? That's crazy!
I was showing this guy rotation matrices, and he seriously asked, "What's a degree? Is that like pi/180?" --rwg
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com
Sorry, I meant mixed numbers. In my mind, they're the improper thing... On Thu, Dec 10, 2015 at 7:54 AM, Mike Stay <metaweta@gmail.com> wrote:
I think the only good thing about improper fractions is that they're an intermediate stage in continued fractions.
On Thu, Dec 10, 2015 at 7:37 AM, Dan Asimov <dasimov@earthlink.net> wrote:
At least in grade school, I was likewise required to convert fractions to mixed form. I agree that automatically doing this (and calling the raw ratio "improper") is pretty silly.
Still, if you need to know the size of a number you will care about knowing at least approximately the integer part. So it's not just unadulterated nonsense.
—Dan
On Dec 10, 2015, at 3:50 AM, Bill Gosper <billgosper@gmail.com> wrote:
A young friend has to convert all his "improper" fractions to mixed numbers. When he repeated my remark that mathematicians, scientists, and engineers shun mixed numbers, he got hauled up before the dean, who angrily insisted that mathematicians actually prefer mixed numbers. Does anybody know a computer algebra system that even offers mixed numbers as an output format? An input format?? --rwg A still younger friend emailed:
What?? 3½=3+½?? That's crazy!
I was showing this guy rotation matrices, and he seriously asked, "What's a degree? Is that like pi/180?" --rwg
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com
-- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com
How about carpenters? "I need this board cut to be three feet, seven and five-eights inches long." On Dec 10, 2015 12:11 PM, "Mike Stay" <metaweta@gmail.com> wrote:
Sorry, I meant mixed numbers. In my mind, they're the improper thing...
On Thu, Dec 10, 2015 at 7:54 AM, Mike Stay <metaweta@gmail.com> wrote:
I think the only good thing about improper fractions is that they're an intermediate stage in continued fractions.
On Thu, Dec 10, 2015 at 7:37 AM, Dan Asimov <dasimov@earthlink.net> wrote:
At least in grade school, I was likewise required to convert fractions to mixed form. I agree that automatically doing this (and calling the raw ratio "improper") is pretty silly.
Still, if you need to know the size of a number you will care about knowing at least approximately the integer part. So it's not just unadulterated nonsense.
—Dan
On Dec 10, 2015, at 3:50 AM, Bill Gosper <billgosper@gmail.com> wrote:
A young friend has to convert all his "improper" fractions to mixed numbers. When he repeated my remark that mathematicians, scientists, and engineers shun mixed numbers, he got hauled up before the dean, who angrily insisted that mathematicians actually prefer mixed numbers. Does anybody know a computer algebra system that even offers mixed numbers as an output format? An input format?? --rwg A still younger friend emailed:
What?? 3½=3+½?? That's crazy!
I was showing this guy rotation matrices, and he seriously asked, "What's a degree? Is that like pi/180?" --rwg
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com
-- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
Would you believe carpenters use "five quarter round" molding? --rwg On 2015-12-14 15:07, William R. Somsky wrote:
How about carpenters? "I need this board cut to be three feet, seven and five-eights inches long." On Dec 10, 2015 12:11 PM, "Mike Stay" <metaweta@gmail.com> wrote:
Sorry, I meant mixed numbers. In my mind, they're the improper thing...
On Thu, Dec 10, 2015 at 7:54 AM, Mike Stay <metaweta@gmail.com> wrote:
I think the only good thing about improper fractions is that they're an intermediate stage in continued fractions.
On Thu, Dec 10, 2015 at 7:37 AM, Dan Asimov <dasimov@earthlink.net> wrote:
At least in grade school, I was likewise required to convert fractions to mixed form. I agree that automatically doing this (and calling the raw ratio "improper") is pretty silly.
Still, if you need to know the size of a number you will care about knowing at least approximately the integer part. So it's not just unadulterated nonsense.
—Dan
On Dec 10, 2015, at 3:50 AM, Bill Gosper <billgosper@gmail.com> wrote:
A young friend has to convert all his "improper" fractions to mixed numbers. When he repeated my remark that mathematicians, scientists, and engineers shun mixed numbers, he got hauled up before the dean, who angrily insisted that mathematicians actually prefer mixed numbers. Does anybody know a computer algebra system that even offers mixed numbers as an output format? An input format?? --rwg A still younger friend emailed:
What?? 3½=3+½?? That's crazy!
I was showing this guy rotation matrices, and he seriously asked, "What's a degree? Is that like pi/180?" --rwg
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com
-- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com
According to something I've read, Legendre asserted that: ----- If p_n denotes the nth prime, then for any integer K at least one of the odd integers 2K + 1, 2K + 3, . . ., 2K + 2p_(n-1) + 1 is not divisible by any of the primes p_1, p_2, . . ., p_n. ----- It turns out that this is not true. The situation is now completely understood: The set of exactly those p_n for which the statement holds is known. The answer is easy to state but does not seem to be easy to prove, so this is not necessarily good puzzle material. But just in case anyone (who doesn't already know the answer) would like to conjecture the makeup of the set of p_n for which this statement holds, feel free — and I'll post the answer soon. —Dan
You said: The set of exactly those p_n for which the statement holds is known. The answer is easy to state but does not seem to be easy to prove, so this is not necessarily good puzzle material. Me: but would it make a good sequence? What are the first few such primes? If it is not in the OEIS please submit it! Best regards Neil Neil J. A. Sloane, President, OEIS Foundation. 11 South Adelaide Avenue, Highland Park, NJ 08904, USA. Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ. Phone: 732 828 6098; home page: http://NeilSloane.com Email: njasloane@gmail.com On Wed, Dec 16, 2015 at 9:14 PM, Dan Asimov <asimov@msri.org> wrote:
According to something I've read, Legendre asserted that:
----- If p_n denotes the nth prime, then for any integer K at least one of the odd integers
2K + 1, 2K + 3, . . ., 2K + 2p_(n-1) + 1
is not divisible by any of the primes p_1, p_2, . . ., p_n. -----
It turns out that this is not true. The situation is now completely understood: The set of exactly those p_n for which the statement holds is known.
The answer is easy to state but does not seem to be easy to prove, so this is not necessarily good puzzle material.
But just in case anyone (who doesn't already know the answer) would like to conjecture the makeup of the set of p_n for which this statement holds, feel free — and I'll post the answer soon.
—Dan _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
="rwg" <rwg@sdf.org> Would you believe carpenters use "five quarter round" molding? =William R. Somsky How about carpenters? "I need this board cut to be three feet, seven and five-eights inches long."
Oh, those wacky carpenters. Their dimensionality for nail length is in money units, specifically pennies. The measure was once the price per hundred nails of a given length... but actually it was per long-hundred, that is, per 120. Notwithstanding that there are 240 pennies per pound sterling, some fifteenth century structures still stand. Coincidentally today I measured my hat size; I'm a 7 3/8. Happy holidays!
I agree with Dan. If I told you that I'm 669 months old, i.e. 669/12 years old, you'd be justified in feeling that I'm being unhelpful. (When my kids were very young, and it was common for people to inquire about their ages, I would sometimes tell them both my age and theirs, measured in months.) Jim On Thu, Dec 10, 2015 at 10:37 AM, Dan Asimov <dasimov@earthlink.net> wrote:
At least in grade school, I was likewise required to convert fractions to mixed form. I agree that automatically doing this (and calling the raw ratio "improper") is pretty silly.
Still, if you need to know the size of a number you will care about knowing at least approximately the integer part. So it's not just unadulterated nonsense.
—Dan
On Dec 10, 2015, at 3:50 AM, Bill Gosper <billgosper@gmail.com> wrote:
A young friend has to convert all his "improper" fractions to mixed numbers. When he repeated my remark that mathematicians, scientists, and engineers shun mixed numbers, he got hauled up before the dean, who angrily insisted that mathematicians actually prefer mixed numbers. Does anybody know a computer algebra system that even offers mixed numbers as an output format? An input format?? --rwg A still younger friend emailed:
What?? 3½=3+½?? That's crazy!
I was showing this guy rotation matrices, and he seriously asked, "What's a degree? Is that like pi/180?" --rwg
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
I friend of mine assists in the Santa Cruz CA public schools. She reports that a teacher told the class that officially 1 is a prime number, while admitting that mathematicians think otherwise. Bill, since your friend was hauled before the "dean" rather than the "principal", I'm guessing he goes to a private school. That doesn't bode well for the quality of that private school. -- Gene From: Bill Gosper <billgosper@gmail.com> To: math-fun@mailman.xmission.com Sent: Thursday, December 10, 2015 3:50 AM Subject: [math-fun] Mixed numbers? A young friend has to convert all his "improper" fractions to mixed numbers. When he repeated my remark that mathematicians, scientists, and engineers shun mixed numbers, he got hauled up before the dean, who angrily insisted that mathematicians actually prefer mixed numbers. Does anybody know a computer algebra system that even offers mixed numbers as an output format? An input format?? --rwg A still younger friend emailed: What?? 3½=3+½?? That's crazy! I was showing this guy rotation matrices, and he seriously asked, "What's a degree? Is that like pi/180?" --rwg _______________________________________________
participants (12)
-
Allan Wechsler -
Bill Gosper -
Dan Asimov -
Dan Asimov -
Eugene Salamin -
James Propp -
Marc LeBrun -
Mike Stay -
Neil Sloane -
rwg -
Thane Plambeck -
William R. Somsky