Why is the semicubical parabola considered a parabola?
Simple question here.
Why is the semicubical parabola ---defined by the equation $y^2 = a^2 x^3$--- considered a parabola?
If you look at the graph, it looks like a half parabola at best. This contradicts both ways to define a parabola. (I don't consider quadratics and parabolas the same thing.)
conic-sections cubic-equations
edited Nov 29 '18 at 3:38
Blue
47.6k870151
asked Nov 29 '18 at 2:21
Xavier Stanton
319211
add a comment |
Simple question here.
Why is the semicubical parabola ---defined by the equation $y^2 = a^2 x^3$--- considered a parabola?
If you look at the graph, it looks like a half parabola at best. This contradicts both ways to define a parabola. (I don't consider quadratics and parabolas the same thing.)
conic-sections cubic-equations
edited Nov 29 '18 at 3:38
Blue
47.6k870151
asked Nov 29 '18 at 2:21
Xavier Stanton
319211
2
I don't believe the curve is "considered a parabola". It simply has "parabola" as part of its name. (A "koala bear" is not considered a bear, and a "jellyfish" is not considered a fish.) The discoverer, William Neile, may simply have wanted the name to evoke nothing more than the general shape of the figure. (Mathematicians are known to abuse notation and terminology whenever it suits their expository purposes.) Perhaps you should research Neile's 1657 investigation of the curve, to see if he gave a specific reason for coining the term.
– Blue
Nov 29 '18 at 3:52
add a comment |
Simple question here.
Why is the semicubical parabola ---defined by the equation $y^2 = a^2 x^3$--- considered a parabola?
If you look at the graph, it looks like a half parabola at best. This contradicts both ways to define a parabola. (I don't consider quadratics and parabolas the same thing.)
conic-sections cubic-equations
edited Nov 29 '18 at 3:38
Blue
47.6k870151
asked Nov 29 '18 at 2:21
Xavier Stanton
319211
Simple question here.
Why is the semicubical parabola ---defined by the equation $y^2 = a^2 x^3$--- considered a parabola?
If you look at the graph, it looks like a half parabola at best. This contradicts both ways to define a parabola. (I don't consider quadratics and parabolas the same thing.)
conic-sections cubic-equations
conic-sections cubic-equations
edited Nov 29 '18 at 3:38
Blue
47.6k870151
asked Nov 29 '18 at 2:21
Xavier Stanton
319211
edited Nov 29 '18 at 3:38
Blue
47.6k870151
asked Nov 29 '18 at 2:21
Xavier Stanton
319211
edited Nov 29 '18 at 3:38
Blue
47.6k870151
edited Nov 29 '18 at 3:38
Blue
47.6k870151
edited Nov 29 '18 at 3:38
Blue
47.6k870151
47.6k870151
asked Nov 29 '18 at 2:21
Xavier Stanton
319211
asked Nov 29 '18 at 2:21
Xavier Stanton
319211
asked Nov 29 '18 at 2:21
Xavier Stanton
319211
319211
2
I don't believe the curve is "considered a parabola". It simply has "parabola" as part of its name. (A "koala bear" is not considered a bear, and a "jellyfish" is not considered a fish.) The discoverer, William Neile, may simply have wanted the name to evoke nothing more than the general shape of the figure. (Mathematicians are known to abuse notation and terminology whenever it suits their expository purposes.) Perhaps you should research Neile's 1657 investigation of the curve, to see if he gave a specific reason for coining the term.
– Blue
Nov 29 '18 at 3:52
add a comment |
2
I don't believe the curve is "considered a parabola". It simply has "parabola" as part of its name. (A "koala bear" is not considered a bear, and a "jellyfish" is not considered a fish.) The discoverer, William Neile, may simply have wanted the name to evoke nothing more than the general shape of the figure. (Mathematicians are known to abuse notation and terminology whenever it suits their expository purposes.) Perhaps you should research Neile's 1657 investigation of the curve, to see if he gave a specific reason for coining the term.
– Blue
Nov 29 '18 at 3:52
2
2
I don't believe the curve is "considered a parabola". It simply has "parabola" as part of its name. (A "koala bear" is not considered a bear, and a "jellyfish" is not considered a fish.) The discoverer, William Neile, may simply have wanted the name to evoke nothing more than the general shape of the figure. (Mathematicians are known to abuse notation and terminology whenever it suits their expository purposes.) Perhaps you should research Neile's 1657 investigation of the curve, to see if he gave a specific reason for coining the term.
– Blue
Nov 29 '18 at 3:52
I don't believe the curve is "considered a parabola". It simply has "parabola" as part of its name. (A "koala bear" is not considered a bear, and a "jellyfish" is not considered a fish.) The discoverer, William Neile, may simply have wanted the name to evoke nothing more than the general shape of the figure. (Mathematicians are known to abuse notation and terminology whenever it suits their expository purposes.) Perhaps you should research Neile's 1657 investigation of the curve, to see if he gave a specific reason for coining the term.
– Blue
Nov 29 '18 at 3:52
add a comment |
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I don't believe the curve is "considered a parabola". It simply has "parabola" as part of its name. (A "koala bear" is not considered a bear, and a "jellyfish" is not considered a fish.) The discoverer, William Neile, may simply have wanted the name to evoke nothing more than the general shape of the figure. (Mathematicians are known to abuse notation and terminology whenever it suits their expository purposes.) Perhaps you should research Neile's 1657 investigation of the curve, to see if he gave a specific reason for coining the term.
– Blue
Nov 29 '18 at 3:52