You first one put me in the mind of evil world problems this is my favorite:
The headmaster of a provincial boys’ school believes strongly in the great value of
practical experience in forming boys’ minds. It is this that has made up his mind to take the whole form to the Zoological gardens of a great metropolitan city. ‘How else can they pick up the rudiments of Zoological gardening?’ he asks himself — the question is merely rhetorical and does not require an answer, but to show his agreement with the wit and wisdom of the inquirer, the headmaster chuckles softly to himself, and sighs. Alas! Little does he know what lies in store. Because the school has been founded on principles of freedom from fidgety nonsense, no books are kept and it is unknown just what is the size of the form. When people ask how many boys are in the various forms, Dr Chockle-Fervyn answers mildly, ‘Oh, various numbers-I think.’For
the problem that presents itself in a few moments, the fact that the number of boys is unknown takes on great importance. The boys go to the zoo; they see animals;they grow hungry. The tables in the cafeteria seat twelve. For each tableful of boys, the Doctor brings 45
steak pies; not that he has been so fussy as to ask for that number-he merely says to the attendant, ‘A carton or so of hot steak pies, perhaps, please,’ each time he sees a table
of unfed boys. (Afterwards, enquiries in the packing department of Hengist & Horsa Olde Englishe Meat Products produced the number 45. ‘We always puts 45, your honour, sir. The sum
of the hexpounents on the proims bein’ free, you see. Free dimensions, loikspice. Glad to ‘elp your worship.’) When the boys have finished, it is time to feed the lions. This
is done, in the metropolitan zoo to which the problem has reference, by opening the gates between the lion house and the cafeteria; the fact being known in the metropolitan area, only tourists are eaten on most days. Today, the only tourists are the boys from Fervyn Towers
of Learning. Old ‘Chock-full-ofvermin’ is in the 100. The lions lick their whiskers and prowl smugly back to the lion house. ‘Can’t say exactly,’ was the headmaster’s reply to anxious parental enquiries after the hols commenced-and those words, at least, were spoken true. ‘Some
of them may have got lost at the “zoo”, of course. An interesting question. Are you
sure you had a boy here?’
It must not be thought, however, that vagueness went with want of curiosity or with pedagogical apathy in Dr C.-F.-far from it. He went so far as to prevail on the head gardener of the zoological garden to have the stomachs of 25 of the lions pumped, and the contents sorted. ‘Unheard of, sir,’ was the initial reaction of this official; but the good Doctor plied him with educational anecdotes,and reminded him that the schools could not be expected to produce the required quota of zoological gardeners unless the gardeners took an interest in education. The curator (as he was also called) mollified.’Better see to it myself, you know. Can’t trust these young fellows these days. Would the boys benefit by a personal report from myself?’ It was agreed that the results would be presented at assembly in the Great Hall down at Pummidge in the near future. Briefly, it can be stated that every 25 lions managed 18 boys among them.
‘And now, lads,’ said the Doctor after the vote of thanks, ‘I have a practical exercise for you in the multiplication of fractions. How many steak pies were eaten by each lion?
“You know the facts, and you should be able to visualise the problem. Think of
pies inside boys,and boys inside lions. For artistic expression, there is a prize for the most vivid painting of the meal. Those doing military science will show the optimum formations for the armies involved: lion, boy,and pie. For social science
…
Only the arithmetic problem need detain us here. Let m be the rational number corresponding to the meal in which the boys eat and the pies are eaten. Thinking of m as an endomorphism of Q, we have m:45 –>12.
If M is the endomorphism whereby lions eat and boys are eaten, then
M: 18 –> 25. Since these are Z-module endomorphisms we may also write
18 X 45 -m-> 18 X 12 -M-> 25 X 12
SO that the composition Mm sends 810 –> 300. But the rational represented by the fraction 10/27 sends 810 = 30 x 27 to 300 = 30 x 10. If two endomorphisms
of Q agree at a non-zero element of Q, they agree on all of Q, since this amounts to stating that cancellation holds in Q, and since Q is a field.
Thus Mm sends 27 to 10, or Mm = 10/27, or, as we easily see,
27/10 pies went into each lion.In mixed numbers this is 2 7/10
My personal pet peeve that was surely constructed by an evil mathematician: the symbol (2,5) can either refer to a point in the coordinate plane or else the open interval between 2 and 5, depending on the context.
The last one reminds me of something my grandfather used to say: “Professors like to make Calculus look hard so that they will look smart.”
The second reminds me of something I say to my students all the time: “I wish I could get in my time machine, rev it up to 88mph, and go back in time and give a beating to whomever thought using this notation again would be a good idea!”
Comes up when talking about…
~ f(x) does not mean “f times x”
~ f^-1 (x) does not mean “1 / f(x)”
~ (0, 2) can mean the point x=0, y=2 OR it can mean the open interval 0<x<2
that last one remind Man of phrase “it is clear that….” in math textbook. Man say many time that mean “good luck with this….”
2nd Mr Sock Monkey, and would add ‘left as an exercise for the reader’. THank you for exposing this perfidy.
And who the heck used multiplication notation for functions? f(x) could have been expressing something else.
What multiplication notation?
I’m more concerned that xy means x times y, but 2 1/2 means 2 plus 1/2.
You first one put me in the mind of evil world problems this is my favorite:
The headmaster of a provincial boys’ school believes strongly in the great value of
practical experience in forming boys’ minds. It is this that has made up his mind to take the whole form to the Zoological gardens of a great metropolitan city. ‘How else can they pick up the rudiments of Zoological gardening?’ he asks himself — the question is merely rhetorical and does not require an answer, but to show his agreement with the wit and wisdom of the inquirer, the headmaster chuckles softly to himself, and sighs. Alas! Little does he know what lies in store. Because the school has been founded on principles of freedom from fidgety nonsense, no books are kept and it is unknown just what is the size of the form. When people ask how many boys are in the various forms, Dr Chockle-Fervyn answers mildly, ‘Oh, various numbers-I think.’For
the problem that presents itself in a few moments, the fact that the number of boys is unknown takes on great importance. The boys go to the zoo; they see animals;they grow hungry. The tables in the cafeteria seat twelve. For each tableful of boys, the Doctor brings 45
steak pies; not that he has been so fussy as to ask for that number-he merely says to the attendant, ‘A carton or so of hot steak pies, perhaps, please,’ each time he sees a table
of unfed boys. (Afterwards, enquiries in the packing department of Hengist & Horsa Olde Englishe Meat Products produced the number 45. ‘We always puts 45, your honour, sir. The sum
of the hexpounents on the proims bein’ free, you see. Free dimensions, loikspice. Glad to ‘elp your worship.’) When the boys have finished, it is time to feed the lions. This
is done, in the metropolitan zoo to which the problem has reference, by opening the gates between the lion house and the cafeteria; the fact being known in the metropolitan area, only tourists are eaten on most days. Today, the only tourists are the boys from Fervyn Towers
of Learning. Old ‘Chock-full-ofvermin’ is in the 100. The lions lick their whiskers and prowl smugly back to the lion house. ‘Can’t say exactly,’ was the headmaster’s reply to anxious parental enquiries after the hols commenced-and those words, at least, were spoken true. ‘Some
of them may have got lost at the “zoo”, of course. An interesting question. Are you
sure you had a boy here?’
It must not be thought, however, that vagueness went with want of curiosity or with pedagogical apathy in Dr C.-F.-far from it. He went so far as to prevail on the head gardener of the zoological garden to have the stomachs of 25 of the lions pumped, and the contents sorted. ‘Unheard of, sir,’ was the initial reaction of this official; but the good Doctor plied him with educational anecdotes,and reminded him that the schools could not be expected to produce the required quota of zoological gardeners unless the gardeners took an interest in education. The curator (as he was also called) mollified.’Better see to it myself, you know. Can’t trust these young fellows these days. Would the boys benefit by a personal report from myself?’ It was agreed that the results would be presented at assembly in the Great Hall down at Pummidge in the near future. Briefly, it can be stated that every 25 lions managed 18 boys among them.
‘And now, lads,’ said the Doctor after the vote of thanks, ‘I have a practical exercise for you in the multiplication of fractions. How many steak pies were eaten by each lion?
Loved that, Doug M. Do you have a source for where you came across it?
Mathematics made difficult.
2.7?
After reading the problem, I was not quite sure neither of my name nor of the answer.
Not being English my mother tongue, makes this more interesting.
If only it were so simple:
“You know the facts, and you should be able to visualise the problem. Think of
pies inside boys,and boys inside lions. For artistic expression, there is a prize for the most vivid painting of the meal. Those doing military science will show the optimum formations for the armies involved: lion, boy,and pie. For social science
…
Only the arithmetic problem need detain us here. Let m be the rational number corresponding to the meal in which the boys eat and the pies are eaten. Thinking of m as an endomorphism of Q, we have m:45 –>12.
If M is the endomorphism whereby lions eat and boys are eaten, then
M: 18 –> 25. Since these are Z-module endomorphisms we may also write
18 X 45 -m-> 18 X 12 -M-> 25 X 12
SO that the composition Mm sends 810 –> 300. But the rational represented by the fraction 10/27 sends 810 = 30 x 27 to 300 = 30 x 10. If two endomorphisms
of Q agree at a non-zero element of Q, they agree on all of Q, since this amounts to stating that cancellation holds in Q, and since Q is a field.
Thus Mm sends 27 to 10, or Mm = 10/27, or, as we easily see,
27/10 pies went into each lion.In mixed numbers this is 2 7/10
My personal pet peeve that was surely constructed by an evil mathematician: the symbol (2,5) can either refer to a point in the coordinate plane or else the open interval between 2 and 5, depending on the context.
Yeah, that was a blown call. Also, whoever decided “inverse” should share the symbol for “raised to the minus-1 power”.
Haha!! The logic exam is awesome!
I laughed out loud several times while reading this and watching my students work on a science lab.
I think that silly mnemonic is achieving its evil purpose…it needs to be foiled…
These are hilarious!!! The decimal point in the European number especially, grr!!
The last one reminds me of something my grandfather used to say: “Professors like to make Calculus look hard so that they will look smart.”
The second reminds me of something I say to my students all the time: “I wish I could get in my time machine, rev it up to 88mph, and go back in time and give a beating to whomever thought using this notation again would be a good idea!”
Comes up when talking about…
~ f(x) does not mean “f times x”
~ f^-1 (x) does not mean “1 / f(x)”
~ (0, 2) can mean the point x=0, y=2 OR it can mean the open interval 0<x<2
…and so on
I would definitely tag along on your DeLorean trip on any of those topics.
Is the answer to this question ‘no’?
a) yes
b) no
c) nope
I choose c).