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History behind the choice of letters $h$ and $k$ for the vertex of a parabola?
After failing to find a historical explanation for usage of letters $h$ and $k$ for the vertex of a parabola in most relatively recent textbooks in anglosphere, I turn to math.SE.
Is there any historical explanation for usage of these particular letters and if there is, what is it?
math-history conic-sections
edited Mar 20 '14 at 21:56
wanderer
2,4071816
asked Jan 23 '14 at 8:12
2305843008139952128
5329
|
show 3 more comments
After failing to find a historical explanation for usage of letters $h$ and $k$ for the vertex of a parabola in most relatively recent textbooks in anglosphere, I turn to math.SE.
Is there any historical explanation for usage of these particular letters and if there is, what is it?
math-history conic-sections
edited Mar 20 '14 at 21:56
wanderer
2,4071816
asked Jan 23 '14 at 8:12
2305843008139952128
5329
Who exactly uses h and k for the said vertex?
– Mikhail Katz
Jan 23 '14 at 13:21
More or less all textbooks.
– 2305843008139952128
Jan 24 '14 at 12:04
As they say on Wikipedia: The perspective in this question may not represent a worldwide view of the subject. (I looked in a Scandinavian text book and found the vertex to be named $(m,n)$.)
– Per Manne
Jan 24 '14 at 15:08
1
It's not so much that these things are used as the vertex of a parabola. They are used as generic horizontal and vertical shifts. Yes, with parabolas: $y=x^2to y=(x-h)^2+k$, shifting the vertex $(0,0)$ to $(h,k)$, but also in other places, like $x^2+y^2=1to(x-h)^2+(y-k)^2=1$, shifting a circle's center in the same way. I still don't know why these two particular letters though.
– alex.jordan
Jan 25 '14 at 7:18
1
$h$ stands for $h$orizontal; $k$ stands for verti$k$al?
– alex.jordan
Jan 25 '14 at 7:29
|
show 3 more comments
After failing to find a historical explanation for usage of letters $h$ and $k$ for the vertex of a parabola in most relatively recent textbooks in anglosphere, I turn to math.SE.
Is there any historical explanation for usage of these particular letters and if there is, what is it?
math-history conic-sections
edited Mar 20 '14 at 21:56
wanderer
2,4071816
asked Jan 23 '14 at 8:12
2305843008139952128
5329
After failing to find a historical explanation for usage of letters $h$ and $k$ for the vertex of a parabola in most relatively recent textbooks in anglosphere, I turn to math.SE.
Is there any historical explanation for usage of these particular letters and if there is, what is it?
math-history conic-sections
math-history conic-sections
edited Mar 20 '14 at 21:56
wanderer
2,4071816
asked Jan 23 '14 at 8:12
2305843008139952128
5329
edited Mar 20 '14 at 21:56
wanderer
2,4071816
asked Jan 23 '14 at 8:12
2305843008139952128
5329
edited Mar 20 '14 at 21:56
wanderer
2,4071816
edited Mar 20 '14 at 21:56
wanderer
2,4071816
edited Mar 20 '14 at 21:56
wanderer
2,4071816
2,4071816
asked Jan 23 '14 at 8:12
2305843008139952128
5329
asked Jan 23 '14 at 8:12
2305843008139952128
5329
asked Jan 23 '14 at 8:12
2305843008139952128
5329
5329
Who exactly uses h and k for the said vertex?
– Mikhail Katz
Jan 23 '14 at 13:21
More or less all textbooks.
– 2305843008139952128
Jan 24 '14 at 12:04
As they say on Wikipedia: The perspective in this question may not represent a worldwide view of the subject. (I looked in a Scandinavian text book and found the vertex to be named $(m,n)$.)
– Per Manne
Jan 24 '14 at 15:08
1
It's not so much that these things are used as the vertex of a parabola. They are used as generic horizontal and vertical shifts. Yes, with parabolas: $y=x^2to y=(x-h)^2+k$, shifting the vertex $(0,0)$ to $(h,k)$, but also in other places, like $x^2+y^2=1to(x-h)^2+(y-k)^2=1$, shifting a circle's center in the same way. I still don't know why these two particular letters though.
– alex.jordan
Jan 25 '14 at 7:18
1
$h$ stands for $h$orizontal; $k$ stands for verti$k$al?
– alex.jordan
Jan 25 '14 at 7:29
|
show 3 more comments
Who exactly uses h and k for the said vertex?
– Mikhail Katz
Jan 23 '14 at 13:21
More or less all textbooks.
– 2305843008139952128
Jan 24 '14 at 12:04
As they say on Wikipedia: The perspective in this question may not represent a worldwide view of the subject. (I looked in a Scandinavian text book and found the vertex to be named $(m,n)$.)
– Per Manne
Jan 24 '14 at 15:08
1
It's not so much that these things are used as the vertex of a parabola. They are used as generic horizontal and vertical shifts. Yes, with parabolas: $y=x^2to y=(x-h)^2+k$, shifting the vertex $(0,0)$ to $(h,k)$, but also in other places, like $x^2+y^2=1to(x-h)^2+(y-k)^2=1$, shifting a circle's center in the same way. I still don't know why these two particular letters though.
– alex.jordan
Jan 25 '14 at 7:18
1
$h$ stands for $h$orizontal; $k$ stands for verti$k$al?
– alex.jordan
Jan 25 '14 at 7:29
Who exactly uses h and k for the said vertex?
– Mikhail Katz
Jan 23 '14 at 13:21
Who exactly uses h and k for the said vertex?
– Mikhail Katz
Jan 23 '14 at 13:21
More or less all textbooks.
– 2305843008139952128
Jan 24 '14 at 12:04
More or less all textbooks.
– 2305843008139952128
Jan 24 '14 at 12:04
As they say on Wikipedia: The perspective in this question may not represent a worldwide view of the subject. (I looked in a Scandinavian text book and found the vertex to be named $(m,n)$.)
– Per Manne
Jan 24 '14 at 15:08
As they say on Wikipedia: The perspective in this question may not represent a worldwide view of the subject. (I looked in a Scandinavian text book and found the vertex to be named $(m,n)$.)
– Per Manne
Jan 24 '14 at 15:08
1
1
It's not so much that these things are used as the vertex of a parabola. They are used as generic horizontal and vertical shifts. Yes, with parabolas: $y=x^2to y=(x-h)^2+k$, shifting the vertex $(0,0)$ to $(h,k)$, but also in other places, like $x^2+y^2=1to(x-h)^2+(y-k)^2=1$, shifting a circle's center in the same way. I still don't know why these two particular letters though.
– alex.jordan
Jan 25 '14 at 7:18
It's not so much that these things are used as the vertex of a parabola. They are used as generic horizontal and vertical shifts. Yes, with parabolas: $y=x^2to y=(x-h)^2+k$, shifting the vertex $(0,0)$ to $(h,k)$, but also in other places, like $x^2+y^2=1to(x-h)^2+(y-k)^2=1$, shifting a circle's center in the same way. I still don't know why these two particular letters though.
– alex.jordan
Jan 25 '14 at 7:18
1
1
$h$ stands for $h$orizontal; $k$ stands for verti$k$al?
– alex.jordan
Jan 25 '14 at 7:29
$h$ stands for $h$orizontal; $k$ stands for verti$k$al?
– alex.jordan
Jan 25 '14 at 7:29
|
show 3 more comments
2 Answers
2
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oldest
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http://www.latin-dictionary.net/search/latin/kardo7
Making a speculation, one could presume that "k" could refer to Latin "kardo", which when roughly translated, can mean "axis", but more specifically "hinge", which brings us to "h", which is the axis of symmetry.
When looking at the vertex form equation,
if "h" were to stand for "hinge", it would point out the fact that hinges can only pivot horizontally from their base part. With this said, I suppose that "h" shows us how much the line of the graph shifts horizontally on a coordinate plane from the origin.
Looking at "k" again,"k" shows the same thing as "h", but this time vertically.
A synonym that carries the same definition as "kardo" is Latin "tenon". This word directly translates into English "tendon". Tendons help organs shift vertically.
answered Nov 20 '18 at 3:43
Homo Videt
213
You did a really nice job answering this question; I'd encourage you to expand by answering newer questions :)
– Tianlalu
Nov 20 '18 at 4:10
add a comment |
According to http://mathforum.org/library/drmath/view/57023.html
"f" and "g" are used to denote functions, "i" and "j" are used for the imaginary unit, "a" - "e" are used for a lot of various different things. "h" and "k" were just not used for much else. Thus, someone decided that they would be good to use for vertices/centers.
answered Dec 22 '14 at 22:41
dardeshna
362213
add a comment |
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2 Answers
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2 Answers
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active
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http://www.latin-dictionary.net/search/latin/kardo7
Making a speculation, one could presume that "k" could refer to Latin "kardo", which when roughly translated, can mean "axis", but more specifically "hinge", which brings us to "h", which is the axis of symmetry.
When looking at the vertex form equation,
if "h" were to stand for "hinge", it would point out the fact that hinges can only pivot horizontally from their base part. With this said, I suppose that "h" shows us how much the line of the graph shifts horizontally on a coordinate plane from the origin.
Looking at "k" again,"k" shows the same thing as "h", but this time vertically.
A synonym that carries the same definition as "kardo" is Latin "tenon". This word directly translates into English "tendon". Tendons help organs shift vertically.
answered Nov 20 '18 at 3:43
Homo Videt
213
You did a really nice job answering this question; I'd encourage you to expand by answering newer questions :)
– Tianlalu
Nov 20 '18 at 4:10
add a comment |
http://www.latin-dictionary.net/search/latin/kardo7
Making a speculation, one could presume that "k" could refer to Latin "kardo", which when roughly translated, can mean "axis", but more specifically "hinge", which brings us to "h", which is the axis of symmetry.
When looking at the vertex form equation,
if "h" were to stand for "hinge", it would point out the fact that hinges can only pivot horizontally from their base part. With this said, I suppose that "h" shows us how much the line of the graph shifts horizontally on a coordinate plane from the origin.
Looking at "k" again,"k" shows the same thing as "h", but this time vertically.
A synonym that carries the same definition as "kardo" is Latin "tenon". This word directly translates into English "tendon". Tendons help organs shift vertically.
answered Nov 20 '18 at 3:43
Homo Videt
213
You did a really nice job answering this question; I'd encourage you to expand by answering newer questions :)
– Tianlalu
Nov 20 '18 at 4:10
add a comment |
http://www.latin-dictionary.net/search/latin/kardo7
Making a speculation, one could presume that "k" could refer to Latin "kardo", which when roughly translated, can mean "axis", but more specifically "hinge", which brings us to "h", which is the axis of symmetry.
When looking at the vertex form equation,
if "h" were to stand for "hinge", it would point out the fact that hinges can only pivot horizontally from their base part. With this said, I suppose that "h" shows us how much the line of the graph shifts horizontally on a coordinate plane from the origin.
Looking at "k" again,"k" shows the same thing as "h", but this time vertically.
A synonym that carries the same definition as "kardo" is Latin "tenon". This word directly translates into English "tendon". Tendons help organs shift vertically.
answered Nov 20 '18 at 3:43
Homo Videt
213
http://www.latin-dictionary.net/search/latin/kardo7
Making a speculation, one could presume that "k" could refer to Latin "kardo", which when roughly translated, can mean "axis", but more specifically "hinge", which brings us to "h", which is the axis of symmetry.
When looking at the vertex form equation,
if "h" were to stand for "hinge", it would point out the fact that hinges can only pivot horizontally from their base part. With this said, I suppose that "h" shows us how much the line of the graph shifts horizontally on a coordinate plane from the origin.
Looking at "k" again,"k" shows the same thing as "h", but this time vertically.
A synonym that carries the same definition as "kardo" is Latin "tenon". This word directly translates into English "tendon". Tendons help organs shift vertically.
answered Nov 20 '18 at 3:43
Homo Videt
213
answered Nov 20 '18 at 3:43
Homo Videt
213
answered Nov 20 '18 at 3:43
Homo Videt
213
answered Nov 20 '18 at 3:43
Homo Videt
213
213
You did a really nice job answering this question; I'd encourage you to expand by answering newer questions :)
– Tianlalu
Nov 20 '18 at 4:10
add a comment |
You did a really nice job answering this question; I'd encourage you to expand by answering newer questions :)
– Tianlalu
Nov 20 '18 at 4:10
You did a really nice job answering this question; I'd encourage you to expand by answering newer questions :)
– Tianlalu
Nov 20 '18 at 4:10
You did a really nice job answering this question; I'd encourage you to expand by answering newer questions :)
– Tianlalu
Nov 20 '18 at 4:10
add a comment |
According to http://mathforum.org/library/drmath/view/57023.html
"f" and "g" are used to denote functions, "i" and "j" are used for the imaginary unit, "a" - "e" are used for a lot of various different things. "h" and "k" were just not used for much else. Thus, someone decided that they would be good to use for vertices/centers.
answered Dec 22 '14 at 22:41
dardeshna
362213
add a comment |
According to http://mathforum.org/library/drmath/view/57023.html
"f" and "g" are used to denote functions, "i" and "j" are used for the imaginary unit, "a" - "e" are used for a lot of various different things. "h" and "k" were just not used for much else. Thus, someone decided that they would be good to use for vertices/centers.
answered Dec 22 '14 at 22:41
dardeshna
362213
add a comment |
According to http://mathforum.org/library/drmath/view/57023.html
"f" and "g" are used to denote functions, "i" and "j" are used for the imaginary unit, "a" - "e" are used for a lot of various different things. "h" and "k" were just not used for much else. Thus, someone decided that they would be good to use for vertices/centers.
answered Dec 22 '14 at 22:41
dardeshna
362213
According to http://mathforum.org/library/drmath/view/57023.html
"f" and "g" are used to denote functions, "i" and "j" are used for the imaginary unit, "a" - "e" are used for a lot of various different things. "h" and "k" were just not used for much else. Thus, someone decided that they would be good to use for vertices/centers.
answered Dec 22 '14 at 22:41
dardeshna
362213
answered Dec 22 '14 at 22:41
dardeshna
362213
answered Dec 22 '14 at 22:41
dardeshna
362213
answered Dec 22 '14 at 22:41
dardeshna
362213
362213
add a comment |
add a comment |
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Who exactly uses h and k for the said vertex?
– Mikhail Katz
Jan 23 '14 at 13:21
More or less all textbooks.
– 2305843008139952128
Jan 24 '14 at 12:04
As they say on Wikipedia: The perspective in this question may not represent a worldwide view of the subject. (I looked in a Scandinavian text book and found the vertex to be named $(m,n)$.)
– Per Manne
Jan 24 '14 at 15:08
1
It's not so much that these things are used as the vertex of a parabola. They are used as generic horizontal and vertical shifts. Yes, with parabolas: $y=x^2to y=(x-h)^2+k$, shifting the vertex $(0,0)$ to $(h,k)$, but also in other places, like $x^2+y^2=1to(x-h)^2+(y-k)^2=1$, shifting a circle's center in the same way. I still don't know why these two particular letters though.
– alex.jordan
Jan 25 '14 at 7:18
1
$h$ stands for $h$orizontal; $k$ stands for verti$k$al?
– alex.jordan
Jan 25 '14 at 7:29