Important Olympiad-inequalities [duplicate]
$begingroup$
This question already has an answer here:
What are the most popular techniques of proving inequalities?
3 answers
As an olympiad-participant, I've had to solve numerous inequalities; some easy ones and some very difficult ones. Inequalities might appear in every Olympiad discipline (Number theory, Algebra, Geometry and Combinatorics) and usually require previous manipulations, which makes them even harder to solve...
Some time ago, someone told me that
Solving inequalities is kind of applying the same hundred tricks again and again
And in fact, knowledge and experience play a fundamental role when it comes to proving/solving inequalities, rather than instinct.
This is the reason why I wanted to gather the most important Olympiad-inequalities such as
AM-GM (and the weighted one)
Cauchy-Schwarz
Jensen
...
Could you suggest some more?
This question was inspired by the fantastic contributions of @Michael Rozenberg on inequalities.
inequality contest-math big-list
edited Feb 10 at 2:39
Alexander Gruber♦
20.1k25102172
asked Feb 9 at 19:24
Dr. MathvaDr. Mathva
1,668321
$endgroup$
marked as duplicate by Michael Rozenberg inequality
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Feb 10 at 3:18
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
add a comment |
$begingroup$
This question already has an answer here:
What are the most popular techniques of proving inequalities?
3 answers
As an olympiad-participant, I've had to solve numerous inequalities; some easy ones and some very difficult ones. Inequalities might appear in every Olympiad discipline (Number theory, Algebra, Geometry and Combinatorics) and usually require previous manipulations, which makes them even harder to solve...
Some time ago, someone told me that
Solving inequalities is kind of applying the same hundred tricks again and again
And in fact, knowledge and experience play a fundamental role when it comes to proving/solving inequalities, rather than instinct.
This is the reason why I wanted to gather the most important Olympiad-inequalities such as
AM-GM (and the weighted one)
Cauchy-Schwarz
Jensen
...
Could you suggest some more?
This question was inspired by the fantastic contributions of @Michael Rozenberg on inequalities.
inequality contest-math big-list
edited Feb 10 at 2:39
Alexander Gruber♦
20.1k25102172
asked Feb 9 at 19:24
Dr. MathvaDr. Mathva
1,668321
$endgroup$
marked as duplicate by Michael Rozenberg inequality
Users with the inequality badge can single-handedly close inequality questions as duplicates and reopen them as needed.
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Feb 10 at 3:18
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
$begingroup$
@Michael Rozenberg, I know that the question you've linked might look similar to mine; however, I wanted to emphasize the fact that I'm looking for $mathbf{olympiad}$ inequalities, which has nothing to do with the inequalities you might require for the maths-degree for instance...
$endgroup$
– Dr. Mathva
Feb 10 at 11:39
$begingroup$
All these they are Olimpiad inequalities. I think these themes they are same. Remember, there is also IMC.
$endgroup$
– Michael Rozenberg
Feb 10 at 12:42
$begingroup$
@Michael Rozenberg What do you mean by IMC?
$endgroup$
– Dr. Mathva
Feb 10 at 14:22
$begingroup$
See here: imc-math.org.uk
$endgroup$
– Michael Rozenberg
Feb 10 at 14:25
add a comment |
$begingroup$
This question already has an answer here:
What are the most popular techniques of proving inequalities?
3 answers
As an olympiad-participant, I've had to solve numerous inequalities; some easy ones and some very difficult ones. Inequalities might appear in every Olympiad discipline (Number theory, Algebra, Geometry and Combinatorics) and usually require previous manipulations, which makes them even harder to solve...
Some time ago, someone told me that
Solving inequalities is kind of applying the same hundred tricks again and again
And in fact, knowledge and experience play a fundamental role when it comes to proving/solving inequalities, rather than instinct.
This is the reason why I wanted to gather the most important Olympiad-inequalities such as
AM-GM (and the weighted one)
Cauchy-Schwarz
Jensen
...
Could you suggest some more?
This question was inspired by the fantastic contributions of @Michael Rozenberg on inequalities.
inequality contest-math big-list
edited Feb 10 at 2:39
Alexander Gruber♦
20.1k25102172
asked Feb 9 at 19:24
Dr. MathvaDr. Mathva
1,668321
$endgroup$
This question already has an answer here:
What are the most popular techniques of proving inequalities?
3 answers
As an olympiad-participant, I've had to solve numerous inequalities; some easy ones and some very difficult ones. Inequalities might appear in every Olympiad discipline (Number theory, Algebra, Geometry and Combinatorics) and usually require previous manipulations, which makes them even harder to solve...
Some time ago, someone told me that
Solving inequalities is kind of applying the same hundred tricks again and again
And in fact, knowledge and experience play a fundamental role when it comes to proving/solving inequalities, rather than instinct.
This is the reason why I wanted to gather the most important Olympiad-inequalities such as
AM-GM (and the weighted one)
Cauchy-Schwarz
Jensen
...
Could you suggest some more?
This question was inspired by the fantastic contributions of @Michael Rozenberg on inequalities.
This question already has an answer here:
What are the most popular techniques of proving inequalities?
3 answers
inequality contest-math big-list
inequality contest-math big-list
edited Feb 10 at 2:39
Alexander Gruber♦
20.1k25102172
asked Feb 9 at 19:24
Dr. MathvaDr. Mathva
1,668321
edited Feb 10 at 2:39
Alexander Gruber♦
20.1k25102172
asked Feb 9 at 19:24
Dr. MathvaDr. Mathva
1,668321
edited Feb 10 at 2:39
Alexander Gruber♦
20.1k25102172
edited Feb 10 at 2:39
Alexander Gruber♦
20.1k25102172
edited Feb 10 at 2:39
Alexander Gruber♦
20.1k25102172
20.1k25102172
asked Feb 9 at 19:24
Dr. MathvaDr. Mathva
1,668321
asked Feb 9 at 19:24
Dr. MathvaDr. Mathva
1,668321
asked Feb 9 at 19:24
Dr. MathvaDr. Mathva
1,668321
1,668321
marked as duplicate by Michael Rozenberg inequality
Users with the inequality badge can single-handedly close inequality questions as duplicates and reopen them as needed.
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Feb 10 at 3:18
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
marked as duplicate by Michael Rozenberg inequality
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Feb 10 at 3:18
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
$begingroup$
@Michael Rozenberg, I know that the question you've linked might look similar to mine; however, I wanted to emphasize the fact that I'm looking for $mathbf{olympiad}$ inequalities, which has nothing to do with the inequalities you might require for the maths-degree for instance...
$endgroup$
– Dr. Mathva
Feb 10 at 11:39
$begingroup$
All these they are Olimpiad inequalities. I think these themes they are same. Remember, there is also IMC.
$endgroup$
– Michael Rozenberg
Feb 10 at 12:42
$begingroup$
@Michael Rozenberg What do you mean by IMC?
$endgroup$
– Dr. Mathva
Feb 10 at 14:22
$begingroup$
See here: imc-math.org.uk
$endgroup$
– Michael Rozenberg
Feb 10 at 14:25
add a comment |
$begingroup$
@Michael Rozenberg, I know that the question you've linked might look similar to mine; however, I wanted to emphasize the fact that I'm looking for $mathbf{olympiad}$ inequalities, which has nothing to do with the inequalities you might require for the maths-degree for instance...
$endgroup$
– Dr. Mathva
Feb 10 at 11:39
$begingroup$
All these they are Olimpiad inequalities. I think these themes they are same. Remember, there is also IMC.
$endgroup$
– Michael Rozenberg
Feb 10 at 12:42
$begingroup$
@Michael Rozenberg What do you mean by IMC?
$endgroup$
– Dr. Mathva
Feb 10 at 14:22
$begingroup$
See here: imc-math.org.uk
$endgroup$
– Michael Rozenberg
Feb 10 at 14:25
$begingroup$
@Michael Rozenberg, I know that the question you've linked might look similar to mine; however, I wanted to emphasize the fact that I'm looking for $mathbf{olympiad}$ inequalities, which has nothing to do with the inequalities you might require for the maths-degree for instance...
$endgroup$
– Dr. Mathva
Feb 10 at 11:39
$begingroup$
@Michael Rozenberg, I know that the question you've linked might look similar to mine; however, I wanted to emphasize the fact that I'm looking for $mathbf{olympiad}$ inequalities, which has nothing to do with the inequalities you might require for the maths-degree for instance...
$endgroup$
– Dr. Mathva
Feb 10 at 11:39
$begingroup$
All these they are Olimpiad inequalities. I think these themes they are same. Remember, there is also IMC.
$endgroup$
– Michael Rozenberg
Feb 10 at 12:42
$begingroup$
All these they are Olimpiad inequalities. I think these themes they are same. Remember, there is also IMC.
$endgroup$
– Michael Rozenberg
Feb 10 at 12:42
$begingroup$
@Michael Rozenberg What do you mean by IMC?
$endgroup$
– Dr. Mathva
Feb 10 at 14:22
$begingroup$
@Michael Rozenberg What do you mean by IMC?
$endgroup$
– Dr. Mathva
Feb 10 at 14:22
$begingroup$
See here: imc-math.org.uk
$endgroup$
– Michael Rozenberg
Feb 10 at 14:25
$begingroup$
See here: imc-math.org.uk
$endgroup$
– Michael Rozenberg
Feb 10 at 14:25
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
Essential reading:
Olympiad Inequalities, Thomas J. Mildorf
All useful inequalities are clearly listed and explaind on the first few pages. Mildorf calls them "The Standard Dozen":
EDIT: If you look for a good book, here is my favorite one:
The book covers in extensive detail the following topics:
Also a fine reading:
A Brief Introduction to Olympiad Inequalities, Evan Chen
answered Feb 9 at 19:48
OldboyOldboy
8,1801936
$endgroup$
2
$begingroup$
While the reference you provide might be useful, displaying text-as-images makes your answer inaccessible to screenreaders, and hampers the searchability of your answer. It would be preferable if you could summarize (in text) the major important results.
$endgroup$
– Xander Henderson
Feb 11 at 18:00
add a comment |
$begingroup$
I did not find a link, but I wrote about this theme already.
I'll write something again.
There are many methods:
Cauchy-Schwarz (C-S)
AM-GM
Holder
Jensen
Minkowski
Maclaurin
Rearrangement
Chebyshov
Muirhead
Karamata
Lagrange multipliers
Buffalo Way (BW)
Contradiction
Tangent Line method
Schur
Sum Of Squares (SOS)
Schur-SOS method (S-S)
Bernoulli
Bacteria
RCF, LCF, HCF (with half convex, half concave functions) by V.Cirtoaje
E-V Method by V.Cirtoaje
uvw
Inequalities like Schur
pRr method for the geometric inequalities
and more.
In my opinion, the best book it's the inequalities forum in the AoPS: https://artofproblemsolving.com/community/c6t243f6_inequalities
Just read it!
Also, there is the last book by Vasile Cirtoaje (2018) and his papers.
An example for using pRr.
Let $a$, $b$ and $c$ be sides-lengths of a triangle. Prove that:
$$a^3+b^3+c^3-a^2b-a^2c-b^2a-b^2c-c^2a-c^2b+3abcgeq0.$$
Proof:
It's $$Rgeq2r,$$ which is obvious.
Actually, the inequality $$sum_{cyc}(a^3-a^2b-a^2c+abc)geq0$$ is true for all non-negatives $a$, $b$ and $c$ and named as the Schur's inequality.
answered Feb 9 at 20:50
Michael RozenbergMichael Rozenberg
103k1891196
$endgroup$
$begingroup$
Similar to this, which was also written by OP
$endgroup$
– user574848
Feb 10 at 1:54
$begingroup$
This is the link. Thank you!
$endgroup$
– Michael Rozenberg
Feb 10 at 3:17
$begingroup$
Not that it's very important, but you're missing a dot after 16 which has kind of given a bad look to the list. :P Also, what is the pRr method? I googled it but ended up with results in biology which I don't think are very relevant. It's hard to find relevant results about some of the acronyms you used on Google. Don't even get me started on "Bacteria". :P
$endgroup$
– stressed out
Feb 10 at 12:16
$begingroup$
@stressed out I added something. See now. About Bacteria see here: math.stackexchange.com/questions/2903914
$endgroup$
– Michael Rozenberg
Feb 10 at 12:52
1
$begingroup$
@stressed out Yes, of course! But it's a semi-perimeter. Sometimes it's very useful.
$endgroup$
– Michael Rozenberg
Feb 10 at 12:58
|
show 1 more comment
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Essential reading:
Olympiad Inequalities, Thomas J. Mildorf
All useful inequalities are clearly listed and explaind on the first few pages. Mildorf calls them "The Standard Dozen":
EDIT: If you look for a good book, here is my favorite one:
The book covers in extensive detail the following topics:
Also a fine reading:
A Brief Introduction to Olympiad Inequalities, Evan Chen
answered Feb 9 at 19:48
OldboyOldboy
8,1801936
$endgroup$
2
$begingroup$
While the reference you provide might be useful, displaying text-as-images makes your answer inaccessible to screenreaders, and hampers the searchability of your answer. It would be preferable if you could summarize (in text) the major important results.
$endgroup$
– Xander Henderson
Feb 11 at 18:00
add a comment |
$begingroup$
Essential reading:
Olympiad Inequalities, Thomas J. Mildorf
All useful inequalities are clearly listed and explaind on the first few pages. Mildorf calls them "The Standard Dozen":
EDIT: If you look for a good book, here is my favorite one:
The book covers in extensive detail the following topics:
Also a fine reading:
A Brief Introduction to Olympiad Inequalities, Evan Chen
answered Feb 9 at 19:48
OldboyOldboy
8,1801936
$endgroup$
2
$begingroup$
While the reference you provide might be useful, displaying text-as-images makes your answer inaccessible to screenreaders, and hampers the searchability of your answer. It would be preferable if you could summarize (in text) the major important results.
$endgroup$
– Xander Henderson
Feb 11 at 18:00
add a comment |
$begingroup$
Essential reading:
Olympiad Inequalities, Thomas J. Mildorf
All useful inequalities are clearly listed and explaind on the first few pages. Mildorf calls them "The Standard Dozen":
EDIT: If you look for a good book, here is my favorite one:
The book covers in extensive detail the following topics:
Also a fine reading:
A Brief Introduction to Olympiad Inequalities, Evan Chen
answered Feb 9 at 19:48
OldboyOldboy
8,1801936
$endgroup$
Essential reading:
Olympiad Inequalities, Thomas J. Mildorf
All useful inequalities are clearly listed and explaind on the first few pages. Mildorf calls them "The Standard Dozen":
EDIT: If you look for a good book, here is my favorite one:
The book covers in extensive detail the following topics:
Also a fine reading:
A Brief Introduction to Olympiad Inequalities, Evan Chen
answered Feb 9 at 19:48
OldboyOldboy
8,1801936
edited Feb 10 at 19:31
answered Feb 9 at 19:48
OldboyOldboy
8,1801936
answered Feb 9 at 19:48
OldboyOldboy
8,1801936
answered Feb 9 at 19:48
OldboyOldboy
8,1801936
8,1801936
2
$begingroup$
While the reference you provide might be useful, displaying text-as-images makes your answer inaccessible to screenreaders, and hampers the searchability of your answer. It would be preferable if you could summarize (in text) the major important results.
$endgroup$
– Xander Henderson
Feb 11 at 18:00
add a comment |
2
$begingroup$
While the reference you provide might be useful, displaying text-as-images makes your answer inaccessible to screenreaders, and hampers the searchability of your answer. It would be preferable if you could summarize (in text) the major important results.
$endgroup$
– Xander Henderson
Feb 11 at 18:00
2
2
$begingroup$
While the reference you provide might be useful, displaying text-as-images makes your answer inaccessible to screenreaders, and hampers the searchability of your answer. It would be preferable if you could summarize (in text) the major important results.
$endgroup$
– Xander Henderson
Feb 11 at 18:00
$begingroup$
While the reference you provide might be useful, displaying text-as-images makes your answer inaccessible to screenreaders, and hampers the searchability of your answer. It would be preferable if you could summarize (in text) the major important results.
$endgroup$
– Xander Henderson
Feb 11 at 18:00
add a comment |
$begingroup$
I did not find a link, but I wrote about this theme already.
I'll write something again.
There are many methods:
Cauchy-Schwarz (C-S)
AM-GM
Holder
Jensen
Minkowski
Maclaurin
Rearrangement
Chebyshov
Muirhead
Karamata
Lagrange multipliers
Buffalo Way (BW)
Contradiction
Tangent Line method
Schur
Sum Of Squares (SOS)
Schur-SOS method (S-S)
Bernoulli
Bacteria
RCF, LCF, HCF (with half convex, half concave functions) by V.Cirtoaje
E-V Method by V.Cirtoaje
uvw
Inequalities like Schur
pRr method for the geometric inequalities
and more.
In my opinion, the best book it's the inequalities forum in the AoPS: https://artofproblemsolving.com/community/c6t243f6_inequalities
Just read it!
Also, there is the last book by Vasile Cirtoaje (2018) and his papers.
An example for using pRr.
Let $a$, $b$ and $c$ be sides-lengths of a triangle. Prove that:
$$a^3+b^3+c^3-a^2b-a^2c-b^2a-b^2c-c^2a-c^2b+3abcgeq0.$$
Proof:
It's $$Rgeq2r,$$ which is obvious.
Actually, the inequality $$sum_{cyc}(a^3-a^2b-a^2c+abc)geq0$$ is true for all non-negatives $a$, $b$ and $c$ and named as the Schur's inequality.
answered Feb 9 at 20:50
Michael RozenbergMichael Rozenberg
103k1891196
$endgroup$
$begingroup$
Similar to this, which was also written by OP
$endgroup$
– user574848
Feb 10 at 1:54
$begingroup$
This is the link. Thank you!
$endgroup$
– Michael Rozenberg
Feb 10 at 3:17
$begingroup$
Not that it's very important, but you're missing a dot after 16 which has kind of given a bad look to the list. :P Also, what is the pRr method? I googled it but ended up with results in biology which I don't think are very relevant. It's hard to find relevant results about some of the acronyms you used on Google. Don't even get me started on "Bacteria". :P
$endgroup$
– stressed out
Feb 10 at 12:16
$begingroup$
@stressed out I added something. See now. About Bacteria see here: math.stackexchange.com/questions/2903914
$endgroup$
– Michael Rozenberg
Feb 10 at 12:52
1
$begingroup$
@stressed out Yes, of course! But it's a semi-perimeter. Sometimes it's very useful.
$endgroup$
– Michael Rozenberg
Feb 10 at 12:58
|
show 1 more comment
$begingroup$
I did not find a link, but I wrote about this theme already.
I'll write something again.
There are many methods:
Cauchy-Schwarz (C-S)
AM-GM
Holder
Jensen
Minkowski
Maclaurin
Rearrangement
Chebyshov
Muirhead
Karamata
Lagrange multipliers
Buffalo Way (BW)
Contradiction
Tangent Line method
Schur
Sum Of Squares (SOS)
Schur-SOS method (S-S)
Bernoulli
Bacteria
RCF, LCF, HCF (with half convex, half concave functions) by V.Cirtoaje
E-V Method by V.Cirtoaje
uvw
Inequalities like Schur
pRr method for the geometric inequalities
and more.
In my opinion, the best book it's the inequalities forum in the AoPS: https://artofproblemsolving.com/community/c6t243f6_inequalities
Just read it!
Also, there is the last book by Vasile Cirtoaje (2018) and his papers.
An example for using pRr.
Let $a$, $b$ and $c$ be sides-lengths of a triangle. Prove that:
$$a^3+b^3+c^3-a^2b-a^2c-b^2a-b^2c-c^2a-c^2b+3abcgeq0.$$
Proof:
It's $$Rgeq2r,$$ which is obvious.
Actually, the inequality $$sum_{cyc}(a^3-a^2b-a^2c+abc)geq0$$ is true for all non-negatives $a$, $b$ and $c$ and named as the Schur's inequality.
answered Feb 9 at 20:50
Michael RozenbergMichael Rozenberg
103k1891196
$endgroup$
$begingroup$
Similar to this, which was also written by OP
$endgroup$
– user574848
Feb 10 at 1:54
$begingroup$
This is the link. Thank you!
$endgroup$
– Michael Rozenberg
Feb 10 at 3:17
$begingroup$
Not that it's very important, but you're missing a dot after 16 which has kind of given a bad look to the list. :P Also, what is the pRr method? I googled it but ended up with results in biology which I don't think are very relevant. It's hard to find relevant results about some of the acronyms you used on Google. Don't even get me started on "Bacteria". :P
$endgroup$
– stressed out
Feb 10 at 12:16
$begingroup$
@stressed out I added something. See now. About Bacteria see here: math.stackexchange.com/questions/2903914
$endgroup$
– Michael Rozenberg
Feb 10 at 12:52
1
$begingroup$
@stressed out Yes, of course! But it's a semi-perimeter. Sometimes it's very useful.
$endgroup$
– Michael Rozenberg
Feb 10 at 12:58
|
show 1 more comment
$begingroup$
I did not find a link, but I wrote about this theme already.
I'll write something again.
There are many methods:
Cauchy-Schwarz (C-S)
AM-GM
Holder
Jensen
Minkowski
Maclaurin
Rearrangement
Chebyshov
Muirhead
Karamata
Lagrange multipliers
Buffalo Way (BW)
Contradiction
Tangent Line method
Schur
Sum Of Squares (SOS)
Schur-SOS method (S-S)
Bernoulli
Bacteria
RCF, LCF, HCF (with half convex, half concave functions) by V.Cirtoaje
E-V Method by V.Cirtoaje
uvw
Inequalities like Schur
pRr method for the geometric inequalities
and more.
In my opinion, the best book it's the inequalities forum in the AoPS: https://artofproblemsolving.com/community/c6t243f6_inequalities
Just read it!
Also, there is the last book by Vasile Cirtoaje (2018) and his papers.
An example for using pRr.
Let $a$, $b$ and $c$ be sides-lengths of a triangle. Prove that:
$$a^3+b^3+c^3-a^2b-a^2c-b^2a-b^2c-c^2a-c^2b+3abcgeq0.$$
Proof:
It's $$Rgeq2r,$$ which is obvious.
Actually, the inequality $$sum_{cyc}(a^3-a^2b-a^2c+abc)geq0$$ is true for all non-negatives $a$, $b$ and $c$ and named as the Schur's inequality.
answered Feb 9 at 20:50
Michael RozenbergMichael Rozenberg
103k1891196
$endgroup$
I did not find a link, but I wrote about this theme already.
I'll write something again.
There are many methods:
Cauchy-Schwarz (C-S)
AM-GM
Holder
Jensen
Minkowski
Maclaurin
Rearrangement
Chebyshov
Muirhead
Karamata
Lagrange multipliers
Buffalo Way (BW)
Contradiction
Tangent Line method
Schur
Sum Of Squares (SOS)
Schur-SOS method (S-S)
Bernoulli
Bacteria
RCF, LCF, HCF (with half convex, half concave functions) by V.Cirtoaje
E-V Method by V.Cirtoaje
uvw
Inequalities like Schur
pRr method for the geometric inequalities
and more.
In my opinion, the best book it's the inequalities forum in the AoPS: https://artofproblemsolving.com/community/c6t243f6_inequalities
Just read it!
Also, there is the last book by Vasile Cirtoaje (2018) and his papers.
An example for using pRr.
Let $a$, $b$ and $c$ be sides-lengths of a triangle. Prove that:
$$a^3+b^3+c^3-a^2b-a^2c-b^2a-b^2c-c^2a-c^2b+3abcgeq0.$$
Proof:
It's $$Rgeq2r,$$ which is obvious.
Actually, the inequality $$sum_{cyc}(a^3-a^2b-a^2c+abc)geq0$$ is true for all non-negatives $a$, $b$ and $c$ and named as the Schur's inequality.
answered Feb 9 at 20:50
Michael RozenbergMichael Rozenberg
103k1891196
edited Feb 10 at 12:51
answered Feb 9 at 20:50
Michael RozenbergMichael Rozenberg
103k1891196
answered Feb 9 at 20:50
Michael RozenbergMichael Rozenberg
103k1891196
answered Feb 9 at 20:50
Michael RozenbergMichael Rozenberg
103k1891196
103k1891196
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Similar to this, which was also written by OP
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– user574848
Feb 10 at 1:54
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This is the link. Thank you!
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– Michael Rozenberg
Feb 10 at 3:17
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Not that it's very important, but you're missing a dot after 16 which has kind of given a bad look to the list. :P Also, what is the pRr method? I googled it but ended up with results in biology which I don't think are very relevant. It's hard to find relevant results about some of the acronyms you used on Google. Don't even get me started on "Bacteria". :P
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– stressed out
Feb 10 at 12:16
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@stressed out I added something. See now. About Bacteria see here: math.stackexchange.com/questions/2903914
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– Michael Rozenberg
Feb 10 at 12:52
1
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@stressed out Yes, of course! But it's a semi-perimeter. Sometimes it's very useful.
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– Michael Rozenberg
Feb 10 at 12:58
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show 1 more comment
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Similar to this, which was also written by OP
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– user574848
Feb 10 at 1:54
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This is the link. Thank you!
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– Michael Rozenberg
Feb 10 at 3:17
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Not that it's very important, but you're missing a dot after 16 which has kind of given a bad look to the list. :P Also, what is the pRr method? I googled it but ended up with results in biology which I don't think are very relevant. It's hard to find relevant results about some of the acronyms you used on Google. Don't even get me started on "Bacteria". :P
$endgroup$
– stressed out
Feb 10 at 12:16
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@stressed out I added something. See now. About Bacteria see here: math.stackexchange.com/questions/2903914
$endgroup$
– Michael Rozenberg
Feb 10 at 12:52
1
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@stressed out Yes, of course! But it's a semi-perimeter. Sometimes it's very useful.
$endgroup$
– Michael Rozenberg
Feb 10 at 12:58
$begingroup$
Similar to this, which was also written by OP
$endgroup$
– user574848
Feb 10 at 1:54
$begingroup$
Similar to this, which was also written by OP
$endgroup$
– user574848
Feb 10 at 1:54
$begingroup$
This is the link. Thank you!
$endgroup$
– Michael Rozenberg
Feb 10 at 3:17
$begingroup$
This is the link. Thank you!
$endgroup$
– Michael Rozenberg
Feb 10 at 3:17
$begingroup$
Not that it's very important, but you're missing a dot after 16 which has kind of given a bad look to the list. :P Also, what is the pRr method? I googled it but ended up with results in biology which I don't think are very relevant. It's hard to find relevant results about some of the acronyms you used on Google. Don't even get me started on "Bacteria". :P
$endgroup$
– stressed out
Feb 10 at 12:16
$begingroup$
Not that it's very important, but you're missing a dot after 16 which has kind of given a bad look to the list. :P Also, what is the pRr method? I googled it but ended up with results in biology which I don't think are very relevant. It's hard to find relevant results about some of the acronyms you used on Google. Don't even get me started on "Bacteria". :P
$endgroup$
– stressed out
Feb 10 at 12:16
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@stressed out I added something. See now. About Bacteria see here: math.stackexchange.com/questions/2903914
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– Michael Rozenberg
Feb 10 at 12:52
$begingroup$
@stressed out I added something. See now. About Bacteria see here: math.stackexchange.com/questions/2903914
$endgroup$
– Michael Rozenberg
Feb 10 at 12:52
1
1
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@stressed out Yes, of course! But it's a semi-perimeter. Sometimes it's very useful.
$endgroup$
– Michael Rozenberg
Feb 10 at 12:58
$begingroup$
@stressed out Yes, of course! But it's a semi-perimeter. Sometimes it's very useful.
$endgroup$
– Michael Rozenberg
Feb 10 at 12:58
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show 1 more comment
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@Michael Rozenberg, I know that the question you've linked might look similar to mine; however, I wanted to emphasize the fact that I'm looking for $mathbf{olympiad}$ inequalities, which has nothing to do with the inequalities you might require for the maths-degree for instance...
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– Dr. Mathva
Feb 10 at 11:39
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All these they are Olimpiad inequalities. I think these themes they are same. Remember, there is also IMC.
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– Michael Rozenberg
Feb 10 at 12:42
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@Michael Rozenberg What do you mean by IMC?
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– Dr. Mathva
Feb 10 at 14:22
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See here: imc-math.org.uk
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– Michael Rozenberg
Feb 10 at 14:25