Posted last two times[1][2] one of these stories came around, comment applicable here:
As a preamble there most definitely existed anti-semitism in Soviet Union. I am a Russian living in the US with Jewish family in Russia. This is a throw away account.
With that said, stories of anti-semitism told by Russian Jews in US should not be taken at face value. These folks are subject to a very strong selection bias. Most of them came to the US as refugees who were recognized by the US State Department as being discriminated against for being Jewish in USSR/Russia. Secondly they have interest in maintaining the story anti-seminitism because it validates their narrative and could potentially help their relatives immigrate to the US.
Additionally many stories of anti-semitism that I heard were something a non-jew would experience as well but attributed to anti-semitism. As a personal example, I was at first denied admission to a specialized school in very late Soviet period. They eventually let me in because my mother found out that I had the highest score on the entrance exam of any one. Their excuse was that they had to let the kids who were in the paid summer program at the school first and now the class was full. A Jewish kid's parents would have been told they already have too many Jews in the advanced program. Both cases are just the admissions persons asking for a bribe.
In 1987 I and my friend from school went to Moscow to apply to MATI (Moscovskii Aviatsionno Technologicheskii Institut). I am Jewish, my friend Jewish as well. While in line to submit some additional paperwork, we were approached by an administrator, who walked us to the side, and frankly told us to take our documents somewhere else. As Jews, we would never be admitted to the Institut. no matter what.
We went to one of the more Jewish institutes: MIIT (Moskovskii Institut Zheleznodoroshnogo Transporta). The other Jewish place was Moskovskii Institute Stali i Splavov.
I know nothing of the parent or their experiences. Unfortunately, it fits a pattern. That could be coincidence in the case of this comment, but I think the overall pattern is worth pointing out:
A common response to reports of any kind of discrimination is to downplay them -- it's not as bad as people report, they are a little paranoid, exaggerating, spreading stories, etc. If you watch for the pattern you can see it happenning a lot.
It's good, old fashioned FUD[1]: It minimizes the current issue, and more importantly it creates a situation where there are doubts about the credibility any future reporters of discrimination and problems. Finally, it's easy, when it doesn't affect you, to say someone else's problems are no big deal, they're just exaggerating, etc. 'Comedy is you fall down a manhole; tragedy is I stub my toe'.
In my experience, the truth is the opposite of what the FUD says: Discrimination is vastly underplayed, not exaggerated. Think how often the story you read is about a practice that's gone on for years or decades, and you had no idea. The group facing discrimination has much less of a voice, they don't control the media and movies aren't made about their experiences, and they are intimidated into not speaking out (partly due to comments like the ones I'm criticizing: The majority will simply discredit and smear them anyway).
-----
I'll also add that the parent comment fits another pattern: It's all anecdote. It's all based on hypothesis, and subjective analysis and impressions with no real basis.
Furthermore, when people are described as refugees from anti-Semitism, without going into specifics, this gives a very different impression to the public, than when they are described as people moving away due to the same kind of discrimination that Asian Americans face in university admissions.
It's the lack of direct comparisons, which in turn follows from the lack of specifics, that allows people to get an exaggerated sense of the extent of anti-Semitism.
A large number of my friends who are jewish Russian immigrants. I literally only know one Eastern European gentile. He claims everyone wanted to leave the Soviet Union.
I think churches also sponsored Russian immigrants in the 80s and 90s.
Update: I found this site[1].
Both the tsarist Russian and Soviet governments placed restrictions on emigration. In 1885 the imperial Russian government passed a decree that prohibited all emigration except that of Poles and Jews, which explains the small numbers of non-Jewish Russians in the United States before World War I. By the early 1920s, the Bolshevik/communist-led Soviet government implemented further controls that effectively banned all emigration. As for the second-wave White Russian refugees who fled between 1920 and 1922, they were stripped of their citizenship in absentia and could never legally return home. This situation was the same for the post-World War II DPs, who were viewed as Nazi collaborators and traitors by the Soviet authorities.
In contrast, the fourth wave of Russian immigration that began in late 1969 was legal. It was formally limited to Jews, who were allowed to leave the Soviet Union for Israel as part of the agreements reached between the United States and the Soviet Union during the era of détente. In return for allowing Jews to leave, the United States and other western powers expanded the economic, cultural, and intellectual ties with their communist rival. Although Jews leaving the Soviet Union were only granted permission to go to Israel, many had the United States as their true goal; and by 1985 nearly 300,000 had reached the United States.
After 1985 the more liberal policy of the Soviet government under Mikhail Gorbachev allowed anyone to leave the Soviet Union, and thousands more Jewish and non-Jewish Russians immigrated to the United States. Because Russia is an independent country with a democratically elected government, newcomers cannot justify their claim to emigrate on the grounds of political or religious persecution. This has resulted in a slowing of Russian emigration during the last decade of the twentieth century.
Reminds me of when I am in my car at a stop light and a man looks over at me. I always think "wow if I was a woman or if I was black I would think that that is the reason they are looking at me".
My math teacher in Lithuania mentioned that back in his days (50-s) it was practically impossible for a non-Jewish student to get into any math- or physics-related faculty: Jewish families had a very strong multi-generational tradition of both in-school and additional education. He also said he was the only non-jewish in his group in Moscow State University that year.
So at some point it was decided to, ehm, discriminate jewish - they were supposed to be a minority in all the main universities/institutes, under 10%, I think, although this is not a precise number.
Note that I don't advocate anything or anyone, this is just the way it was.
In the early 1900s, Harvard was on track to be a Jewish dominated university, and they made the (then common) decision to limit Jewish enrollment.[1] In reading that article, I learned that even Richard Feynman was affected by Columbia's quota, and ended up at MIT instead. (Go MIT!) Non-meritocratic quotas exist to this day at all elite US universities, with one exception: Caltech.[2]
I know a Jewish family that, in the middle of the 20th century, changed their last name to something not associated with Judaism so that their children could get into college. Imagine having to hide your religion as a way of life, treated by society as if you were hiding a dirty secret.
A similar story[1] was told by the mathematician Edward Frenkel. He was a Jew in Russia and took an exam with "hard" math problems designed to prevent his admission into Moscow State University. It's possible the problems shown in the paper are the ones Frenkel saw since he was a teenager during that time period. (The Cornell paper does not specifically mention Frenkel.)
Having graduated math-oriented Moscow high school that, on one hand, had a lot of graduates go to the math department (roughly translated as MechMath) of MSU (usually, most of the math class alumni goes there), and on the other, had untypical amount of jewish students, these rings so close to home. Hell, I think they actually gave us most part of these problems in math lessons.
Edit: another curious source
> Mikhail Brin decided to study mathematics instead, and was offered a place although the entry exams for Jews were sat separately, in rooms that were notoriously known as "the gas chambers."
I thought he was a biochemist and taught at a med school. Wikipedia says he started writing scifi at 11, and I doubt even he was eligible for med school at that age.
Jews, and many other minority groups, form tight communities were they look out for each other help each other out. So Jewish businesses and organizations tend to discriminate in hiring, recommendations, etc. Happens all the time, very overtly. Since at this point Jewish organizations and businesses in the US are long established and powerful in many areas, this anti-gentile discrimination is problematic to society at large. But it's a type of discrimination that is rarely mentioned and complained about.
Less than 50 years ago, it was legal to discriminate against all minorities. And some of my older Jewish Americans friends can give awful examples. They still don't feel save in the US. You might think it's irrational, but discrimination scars. Minorities are forced to form tight communities.
The majority tribe also looks out for its own. Something like 70+% of white people don't have nonwhite friends. We are wired to seek our own, so exclusion is the default human behavior. I have a dream that one day we will overcome this silly little thing called tribalism. :)
While we're discussing this subject, and hoping to shine a bright light away from all the negativity, the solidarity of the Jewish people is amazing and unequalled! Jews seem to show great compassion and provide unconditional help for their own.
There's wisdom to be gleaned from this I'm sure...
A bit preachy, sorry: Everyone frowns on discrimination by others, people in different times and/or places, but much more important than criticizing others is to do the right thing ourselves. We need to look in the mirror (myself included!).
To choose a prominent example, open discrimination against people who believe in Islam is socially acceptable in much of Western society. How stupid can we be? We're blatently repeating the exact same mistakes as before, the exact thing we frown upon. Some will say, 'but this time is different; we have a valid reason' - which of course is exactly what people said all those previous times, it's just a justification for acting out on fear (and it's just dumb reasoning). The old fears and rationalizations look absurd to us now but seemed just as real at the time as our current fears. Ours will look just as absurd in the future.
Why can't we just apply the simple, blanket rule? Don't discriminate; prejudice is cruel, unjust and unfair, and it results in very bad things. It provides no real benefits. It always ends up on the wrong side of history; the accomplishments and heroes we honor are never hate and the hateful, but those that stood up against them. When our descendents look back at us, which side will we be on?
> We're blatently repeating the exact same mistakes as before, the exact thing we frown upon.
I find it enlightening. Why did people let the nazis take the jews away? Why did people support slavery, even turn escaped slaves in, for money? Why did they allow lynchings to happen?
Well, now we know. Now we understand. Maybe we can view our ancestors in a different light now.
I've been reading US immigration history for various groups. Each group suffered, assimilated, and then promptly shat on the next group. History repeats.
Things are better now because of civil rights. Discrimination is less violent. But things could be better.
Similar events happened in London in the mid-19th century. University College London (UCL), now one of the best colleges in the University of London, was founded to allow students entry through non-religious means. Consequently, it was the first college in the university to allow equal entry to both Jews and women.
This is why British fee-paying schools are called 'public schools', by the way --- they're open to any member of the public who can pay, rather than being open to only a certain subset of the population. Plus public schools were under public management (a board of governors).
I believe there still are some private schools (UK sense) in the UK, but I can't find any references.
Without the alternative easier exams to compare with and the grading scheme that were used, these problems do not mean much regarding the discrimination that took place. It is quite common to give good grades even when the exercises have not been solved completely, but interesting thoughts and ideas have been exposed, especially in mathematics.
Off topic, but regarding problem 2, a math professor once told me of a PhD student who started studying this kind of functions. He spent some time to discover their many interesting properties, until the professor made him understand why these functions were so regular, and that he had actually wasted his time. Funny to see this again.
I wonder why are Askhenazi Jews apparently more intelligent on average... seems that genetics is the main factor, not culture, but I can imagine research in this area is discouraged and controversial.
Something must have happened during the Middle Ages - in antiquity, the Jews weren't regarded as particularly intelligent compared to other groups - that title went to the Ionian Greeks. There's a hypothesis that medieval restrictions on Jewish occupations & land ownership + Christian restrictions on charging interest pushed Jewish people into financial / lending roles in which intelligence was an advantage (meanwhile, many of the smartest Christian men went into the priesthood with its official celibacy). So you had selection on intelligence genes. Further evidence for this hypothesis is the raft of genetic diseases that disproportionately affect Jews, and are related to brain/nerve development - Canavan disease, familial dysautonomia, Joubert Syndrome, MLIV, Niemann-Pick Disease, Spinal muscular atrophy, Tay-Sachs disease, etc. It's possible that being a carrier for some of those provides some sort of boost to intelligence / brain functioning - otherwise you would expect them to be much less common.
Key word in that sentence would be "apparently" (although feel free to provide hard data backing that claim).
A just as probable explanation (and equally controversial and possibly discouraged)would be that Ashkenazi Jews may or may not have acquired a disproportionate influence (wrt to the %age of the population they comprise), allowing them to be over-represented in certain fields giving them the appearance of being "more intelligent on average"?
If you read the book Perfect Rigor, about Grigori Perelman (solved the Poincare Conjecture - won the fields metal, but would not accept the 1MM dollar prize on principle) they tell multiple tails of anti-semitism in the Russian math departments at the time. According to the book, Perelman was basically really lucky to be born when he was and where he was, and that is really the only reason he was given a chance to get the education he got. The world is obviously a better place for guys like this.
The upper bound is clearly x=1 because the square roots cease to exist for x > 1 and and substituting in x = 1 - epsilon^2 gives to first order (8 e + 1) <= (11 - 16 e) which works because 8 <= 11. Does this thing have a root in [0, 1]?
The inverse of y = sqrt(1 + x)/sqrt(1 - x) is with some work x = (y^2 - 1)/(y^2 + 1) so when we divide through by sqrt(1-x) which we know now to be positive, and replace the above, we find:
(y^2 - 1)/(y^2 + 1) * (8 + y) = 11 y - 16
Expanding out we're looking for a root of
-10 y^3 + 24*y^2 - 12 y + 8 = 0
Dividing by -2 to normalize somewhat:
5 y^3 - 12 y^2 + 6 y - 4 = 0
At this point I almost gave up (since it's a cubic and I had no guarantee that x was rational) but got lucky, I started trying positive integers to see where this transitions from negative (y=0) to positive (5y^3) and accidentally found that y=2 solves the equation. Sending it back through I find 3/5, so assuming that it doesn't double back somewhere in the interval [3/5, 1] that's the interval that we're looking for. Phew!
2. Find all functions F(x) : R -> R having the propery that for any x1 and x2,
F(x1) - F(x2) <= (x1 - x2)^2.
Yeah, if you're just entering a university you're probably not going to get this one. Rewriting x1 as x + dx, x2 as x, then this says F(x + dx) - F(x) <= dx^2. With some limits and the Squeeze theorem, this restricts the functions to be differentiable with derivative zero, so they are constant functions. By inspection that is not just necessary but also sufficient.
3. Given a triangle ABC construct with a straightedge and compass a point K on
AB and a point M on BC such that AK = KM = MC.
This seems in general impossible except for some very specific triangles -- is that true? For example if |AB| = 2 and |BC| = 1, it seems that the only point on AB which could possibly be a candidate for K is the midpoint, with M being B. But the only way that the distance from K to M is the same is if BCK is an equilateral triangle, which requires furthermore that the angle BAC is 60 degrees, no?
4. Solve 2 cubert(2y - 1) = y^3 + 1 for real y.
So y = 1 is an obvious solution. Cubing both sides we get
At this point I got stuck and turned to automated tools, which say that this is factorizable as:
(y^2 + y - 1)(y^6 + 2 y^4 + 2 y^3 + 4 y^2 + 2 y + 9)
Graphing the right hand side it seems to be consistently positive, so that just leaves the left hand side, which is -1/2 +/- sqrt(5)/2. That's pretty difficult.
Only to undesirables. Entry exams at mechmath are composed of written and oral stages; these are the questions asked by examiners at oral stage of examination, one on one with potential student.
Only to the undesirables students. Quoting the paper,
"The Mathematics Department of Moscow State University, the most prestigious mathematics school in Russia, was at that time actively trying to keep Jewish students (and other 'undesirables') from enrolling in the department.
One of the methods they used for doing this was to give the unwanted students a different set of problems on their oral exam."
[+] [-] PRJIUS2|10 years ago|reply
As a preamble there most definitely existed anti-semitism in Soviet Union. I am a Russian living in the US with Jewish family in Russia. This is a throw away account.
With that said, stories of anti-semitism told by Russian Jews in US should not be taken at face value. These folks are subject to a very strong selection bias. Most of them came to the US as refugees who were recognized by the US State Department as being discriminated against for being Jewish in USSR/Russia. Secondly they have interest in maintaining the story anti-seminitism because it validates their narrative and could potentially help their relatives immigrate to the US.
Additionally many stories of anti-semitism that I heard were something a non-jew would experience as well but attributed to anti-semitism. As a personal example, I was at first denied admission to a specialized school in very late Soviet period. They eventually let me in because my mother found out that I had the highest score on the entrance exam of any one. Their excuse was that they had to let the kids who were in the paid summer program at the school first and now the class was full. A Jewish kid's parents would have been told they already have too many Jews in the advanced program. Both cases are just the admissions persons asking for a bribe.
[1] https://news.ycombinator.com/item?id=4752047 [2] https://news.ycombinator.com/item?id=5340553
[+] [-] mudil|10 years ago|reply
We went to one of the more Jewish institutes: MIIT (Moskovskii Institut Zheleznodoroshnogo Transporta). The other Jewish place was Moskovskii Institute Stali i Splavov.
[+] [-] hackuser|10 years ago|reply
A common response to reports of any kind of discrimination is to downplay them -- it's not as bad as people report, they are a little paranoid, exaggerating, spreading stories, etc. If you watch for the pattern you can see it happenning a lot.
It's good, old fashioned FUD[1]: It minimizes the current issue, and more importantly it creates a situation where there are doubts about the credibility any future reporters of discrimination and problems. Finally, it's easy, when it doesn't affect you, to say someone else's problems are no big deal, they're just exaggerating, etc. 'Comedy is you fall down a manhole; tragedy is I stub my toe'.
In my experience, the truth is the opposite of what the FUD says: Discrimination is vastly underplayed, not exaggerated. Think how often the story you read is about a practice that's gone on for years or decades, and you had no idea. The group facing discrimination has much less of a voice, they don't control the media and movies aren't made about their experiences, and they are intimidated into not speaking out (partly due to comments like the ones I'm criticizing: The majority will simply discredit and smear them anyway).
-----
I'll also add that the parent comment fits another pattern: It's all anecdote. It's all based on hypothesis, and subjective analysis and impressions with no real basis.
-----
[1] https://en.wikipedia.org/wiki/Fear,_uncertainty_and_doubt
[+] [-] force_reboot|10 years ago|reply
It's the lack of direct comparisons, which in turn follows from the lack of specifics, that allows people to get an exaggerated sense of the extent of anti-Semitism.
[+] [-] kelukelugames|10 years ago|reply
I think churches also sponsored Russian immigrants in the 80s and 90s.
Update: I found this site[1].
Both the tsarist Russian and Soviet governments placed restrictions on emigration. In 1885 the imperial Russian government passed a decree that prohibited all emigration except that of Poles and Jews, which explains the small numbers of non-Jewish Russians in the United States before World War I. By the early 1920s, the Bolshevik/communist-led Soviet government implemented further controls that effectively banned all emigration. As for the second-wave White Russian refugees who fled between 1920 and 1922, they were stripped of their citizenship in absentia and could never legally return home. This situation was the same for the post-World War II DPs, who were viewed as Nazi collaborators and traitors by the Soviet authorities.
In contrast, the fourth wave of Russian immigration that began in late 1969 was legal. It was formally limited to Jews, who were allowed to leave the Soviet Union for Israel as part of the agreements reached between the United States and the Soviet Union during the era of détente. In return for allowing Jews to leave, the United States and other western powers expanded the economic, cultural, and intellectual ties with their communist rival. Although Jews leaving the Soviet Union were only granted permission to go to Israel, many had the United States as their true goal; and by 1985 nearly 300,000 had reached the United States.
After 1985 the more liberal policy of the Soviet government under Mikhail Gorbachev allowed anyone to leave the Soviet Union, and thousands more Jewish and non-Jewish Russians immigrated to the United States. Because Russia is an independent country with a democratically elected government, newcomers cannot justify their claim to emigrate on the grounds of political or religious persecution. This has resulted in a slowing of Russian emigration during the last decade of the twentieth century.
[1] http://www.everyculture.com/multi/Pa-Sp/Russian-Americans.ht...
Immigration history is fascinating. I'm reading about the other groups here: http://www.everyculture.com/multi/Bu-Dr/index.html
[+] [-] gist|10 years ago|reply
Reminds me of when I am in my car at a stop light and a man looks over at me. I always think "wow if I was a woman or if I was black I would think that that is the reason they are looking at me".
[+] [-] vkazanov|10 years ago|reply
My math teacher in Lithuania mentioned that back in his days (50-s) it was practically impossible for a non-Jewish student to get into any math- or physics-related faculty: Jewish families had a very strong multi-generational tradition of both in-school and additional education. He also said he was the only non-jewish in his group in Moscow State University that year.
So at some point it was decided to, ehm, discriminate jewish - they were supposed to be a minority in all the main universities/institutes, under 10%, I think, although this is not a precise number.
Note that I don't advocate anything or anyone, this is just the way it was.
[+] [-] unknown|10 years ago|reply
[deleted]
[+] [-] Udik|10 years ago|reply
[+] [-] tacon|10 years ago|reply
[1] https://en.wikipedia.org/wiki/Jewish_quota
[2] http://www.mindingthecampus.org/2010/12/why_caltech_is_in_a_...
[+] [-] awl130|10 years ago|reply
[+] [-] Chinjut|10 years ago|reply
[+] [-] hackuser|10 years ago|reply
[+] [-] notdonspaulding|10 years ago|reply
[+] [-] jasode|10 years ago|reply
[1]http://www.amazon.com/Love-Math-Heart-Hidden-Reality/dp/0465...
[+] [-] golergka|10 years ago|reply
Edit: another curious source
> Mikhail Brin decided to study mathematics instead, and was offered a place although the entry exams for Jews were sat separately, in rooms that were notoriously known as "the gas chambers."
http://www.haaretz.com/jewish/2.209/google-co-founder-my-fam...
[+] [-] jkot|10 years ago|reply
[+] [-] Amorymeltzer|10 years ago|reply
1: http://www.washingtonpost.com/wp-dyn/content/article/2009/08...
[+] [-] Kliment|10 years ago|reply
[+] [-] guelo|10 years ago|reply
[+] [-] blisterpeanuts|10 years ago|reply
[+] [-] kelukelugames|10 years ago|reply
Less than 50 years ago, it was legal to discriminate against all minorities. And some of my older Jewish Americans friends can give awful examples. They still don't feel save in the US. You might think it's irrational, but discrimination scars. Minorities are forced to form tight communities.
The majority tribe also looks out for its own. Something like 70+% of white people don't have nonwhite friends. We are wired to seek our own, so exclusion is the default human behavior. I have a dream that one day we will overcome this silly little thing called tribalism. :)
[+] [-] jjoe|10 years ago|reply
There's wisdom to be gleaned from this I'm sure...
[+] [-] frandroid|10 years ago|reply
[deleted]
[+] [-] hackuser|10 years ago|reply
To choose a prominent example, open discrimination against people who believe in Islam is socially acceptable in much of Western society. How stupid can we be? We're blatently repeating the exact same mistakes as before, the exact thing we frown upon. Some will say, 'but this time is different; we have a valid reason' - which of course is exactly what people said all those previous times, it's just a justification for acting out on fear (and it's just dumb reasoning). The old fears and rationalizations look absurd to us now but seemed just as real at the time as our current fears. Ours will look just as absurd in the future.
Why can't we just apply the simple, blanket rule? Don't discriminate; prejudice is cruel, unjust and unfair, and it results in very bad things. It provides no real benefits. It always ends up on the wrong side of history; the accomplishments and heroes we honor are never hate and the hateful, but those that stood up against them. When our descendents look back at us, which side will we be on?
[+] [-] wobbleblob|10 years ago|reply
I find it enlightening. Why did people let the nazis take the jews away? Why did people support slavery, even turn escaped slaves in, for money? Why did they allow lynchings to happen?
Well, now we know. Now we understand. Maybe we can view our ancestors in a different light now.
[+] [-] kelukelugames|10 years ago|reply
Things are better now because of civil rights. Discrimination is less violent. But things could be better.
[+] [-] bb101|10 years ago|reply
[+] [-] david-given|10 years ago|reply
I believe there still are some private schools (UK sense) in the UK, but I can't find any references.
[+] [-] nailer|10 years ago|reply
[+] [-] hiq|10 years ago|reply
Off topic, but regarding problem 2, a math professor once told me of a PhD student who started studying this kind of functions. He spent some time to discover their many interesting properties, until the professor made him understand why these functions were so regular, and that he had actually wasted his time. Funny to see this again.
[+] [-] RivieraKid|10 years ago|reply
[+] [-] defen|10 years ago|reply
[+] [-] rogersmith|10 years ago|reply
A just as probable explanation (and equally controversial and possibly discouraged)would be that Ashkenazi Jews may or may not have acquired a disproportionate influence (wrt to the %age of the population they comprise), allowing them to be over-represented in certain fields giving them the appearance of being "more intelligent on average"?
[+] [-] WildUtah|10 years ago|reply
"Natural history of Ashkenazi Intelligence" by Harpending and Cochran is a good start. http://web.mit.edu/fustflum/documents/papers/AshkenaziIQ.jbi...
(Hint: It's all genetic.)
[+] [-] misiti3780|10 years ago|reply
[+] [-] qrian|10 years ago|reply
[+] [-] drostie|10 years ago|reply
The inverse of y = sqrt(1 + x)/sqrt(1 - x) is with some work x = (y^2 - 1)/(y^2 + 1) so when we divide through by sqrt(1-x) which we know now to be positive, and replace the above, we find:
Expanding out we're looking for a root of Dividing by -2 to normalize somewhat: At this point I almost gave up (since it's a cubic and I had no guarantee that x was rational) but got lucky, I started trying positive integers to see where this transitions from negative (y=0) to positive (5y^3) and accidentally found that y=2 solves the equation. Sending it back through I find 3/5, so assuming that it doesn't double back somewhere in the interval [3/5, 1] that's the interval that we're looking for. Phew! Yeah, if you're just entering a university you're probably not going to get this one. Rewriting x1 as x + dx, x2 as x, then this says F(x + dx) - F(x) <= dx^2. With some limits and the Squeeze theorem, this restricts the functions to be differentiable with derivative zero, so they are constant functions. By inspection that is not just necessary but also sufficient. This seems in general impossible except for some very specific triangles -- is that true? For example if |AB| = 2 and |BC| = 1, it seems that the only point on AB which could possibly be a candidate for K is the midpoint, with M being B. But the only way that the distance from K to M is the same is if BCK is an equilateral triangle, which requires furthermore that the angle BAC is 60 degrees, no? So y = 1 is an obvious solution. Cubing both sides we get Then doing polynomial division by y-1 I get At this point I got stuck and turned to automated tools, which say that this is factorizable as: Graphing the right hand side it seems to be consistently positive, so that just leaves the left hand side, which is -1/2 +/- sqrt(5)/2. That's pretty difficult.[+] [-] RivieraKid|10 years ago|reply
[deleted]
[+] [-] gcb0|10 years ago|reply
[+] [-] golergka|10 years ago|reply
[+] [-] replicant|10 years ago|reply