Mixing
Is there a name to this equation: $(y - a|x|^b)^2 + (cx)^2 = d$?
$begingroup$
While doing a survey of the various equations that generate the universal love symbol, a heart curve, I find that many fit into this parametrised form:
$$(y - a|x|^b)^2 + (cx)^2 = d $$
Where a b c d are parameters.
Is there an existing name to this equation?
Or is this equation being used in some fields of mathematics or physics?
If not, I'll name it Paul Ma's Heart Equation :-)
Examples of a heart curve for the parameters a b c d are:
Set a=0.75 b=1 c=0.75 d=1
Set a=0.6 b=(2/3) c=0.8 d=0.9
And if you set
a=(4/5) b=0.5 c=(4/5) d=(16/25)
it is identical to the equation in the math.stackexchange forum:
An equation that generates a beautiful or unique shape for motivating students in mathematics
My Heart Equation
$(y - a|x|^b)^2 + (cx)^2 = d$
can also be used to deform the heart curve. Examples:
For boomerang: Set a=0.5 b=1 c=0.13 d=1
For circle: Set a=0 b=any c=1 d=1
I have written a light hearted blog on this Heart Equation:
http://onemanadreaming.blogspot.com.au/2014/08/mathematical-equation-of-love-heart.html
where the heart curves are graphed for the above mentioned parameters.
soft-question graphing-functions curves
edited Apr 13 '17 at 12:21
Community♦
1
asked Aug 18 '14 at 16:43
PaulPaul
63
$endgroup$
add a comment |
$begingroup$
While doing a survey of the various equations that generate the universal love symbol, a heart curve, I find that many fit into this parametrised form:
$$(y - a|x|^b)^2 + (cx)^2 = d $$
Where a b c d are parameters.
Is there an existing name to this equation?
Or is this equation being used in some fields of mathematics or physics?
If not, I'll name it Paul Ma's Heart Equation :-)
Examples of a heart curve for the parameters a b c d are:
Set a=0.75 b=1 c=0.75 d=1
Set a=0.6 b=(2/3) c=0.8 d=0.9
And if you set
a=(4/5) b=0.5 c=(4/5) d=(16/25)
it is identical to the equation in the math.stackexchange forum:
An equation that generates a beautiful or unique shape for motivating students in mathematics
My Heart Equation
$(y - a|x|^b)^2 + (cx)^2 = d$
can also be used to deform the heart curve. Examples:
For boomerang: Set a=0.5 b=1 c=0.13 d=1
For circle: Set a=0 b=any c=1 d=1
I have written a light hearted blog on this Heart Equation:
http://onemanadreaming.blogspot.com.au/2014/08/mathematical-equation-of-love-heart.html
where the heart curves are graphed for the above mentioned parameters.
soft-question graphing-functions curves
edited Apr 13 '17 at 12:21
Community♦
1
asked Aug 18 '14 at 16:43
PaulPaul
63
$endgroup$
$begingroup$
To help format questions check out the following link. meta.math.stackexchange.com/questions/5020/…
$endgroup$
– Vincent
Aug 18 '14 at 16:47
add a comment |
$begingroup$
While doing a survey of the various equations that generate the universal love symbol, a heart curve, I find that many fit into this parametrised form:
$$(y - a|x|^b)^2 + (cx)^2 = d $$
Where a b c d are parameters.
Is there an existing name to this equation?
Or is this equation being used in some fields of mathematics or physics?
If not, I'll name it Paul Ma's Heart Equation :-)
Examples of a heart curve for the parameters a b c d are:
Set a=0.75 b=1 c=0.75 d=1
Set a=0.6 b=(2/3) c=0.8 d=0.9
And if you set
a=(4/5) b=0.5 c=(4/5) d=(16/25)
it is identical to the equation in the math.stackexchange forum:
An equation that generates a beautiful or unique shape for motivating students in mathematics
My Heart Equation
$(y - a|x|^b)^2 + (cx)^2 = d$
can also be used to deform the heart curve. Examples:
For boomerang: Set a=0.5 b=1 c=0.13 d=1
For circle: Set a=0 b=any c=1 d=1
I have written a light hearted blog on this Heart Equation:
http://onemanadreaming.blogspot.com.au/2014/08/mathematical-equation-of-love-heart.html
where the heart curves are graphed for the above mentioned parameters.
soft-question graphing-functions curves
edited Apr 13 '17 at 12:21
Community♦
1
asked Aug 18 '14 at 16:43
PaulPaul
63
$endgroup$
While doing a survey of the various equations that generate the universal love symbol, a heart curve, I find that many fit into this parametrised form:
$$(y - a|x|^b)^2 + (cx)^2 = d $$
Where a b c d are parameters.
Is there an existing name to this equation?
Or is this equation being used in some fields of mathematics or physics?
If not, I'll name it Paul Ma's Heart Equation :-)
Examples of a heart curve for the parameters a b c d are:
Set a=0.75 b=1 c=0.75 d=1
Set a=0.6 b=(2/3) c=0.8 d=0.9
And if you set
a=(4/5) b=0.5 c=(4/5) d=(16/25)
it is identical to the equation in the math.stackexchange forum:
An equation that generates a beautiful or unique shape for motivating students in mathematics
My Heart Equation
$(y - a|x|^b)^2 + (cx)^2 = d$
can also be used to deform the heart curve. Examples:
For boomerang: Set a=0.5 b=1 c=0.13 d=1
For circle: Set a=0 b=any c=1 d=1
I have written a light hearted blog on this Heart Equation:
http://onemanadreaming.blogspot.com.au/2014/08/mathematical-equation-of-love-heart.html
where the heart curves are graphed for the above mentioned parameters.
soft-question graphing-functions curves
soft-question graphing-functions curves
edited Apr 13 '17 at 12:21
Community♦
1
asked Aug 18 '14 at 16:43
PaulPaul
63
edited Apr 13 '17 at 12:21
Community♦
1
asked Aug 18 '14 at 16:43
PaulPaul
63
edited Apr 13 '17 at 12:21
Community♦
1
edited Apr 13 '17 at 12:21
Community♦
1
edited Apr 13 '17 at 12:21
Community♦
1
1
asked Aug 18 '14 at 16:43
PaulPaul
63
asked Aug 18 '14 at 16:43
PaulPaul
63
asked Aug 18 '14 at 16:43
PaulPaul
63
63
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To help format questions check out the following link. meta.math.stackexchange.com/questions/5020/…
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– Vincent
Aug 18 '14 at 16:47
add a comment |
$begingroup$
To help format questions check out the following link. meta.math.stackexchange.com/questions/5020/…
$endgroup$
– Vincent
Aug 18 '14 at 16:47
$begingroup$
To help format questions check out the following link. meta.math.stackexchange.com/questions/5020/…
$endgroup$
– Vincent
Aug 18 '14 at 16:47
$begingroup$
To help format questions check out the following link. meta.math.stackexchange.com/questions/5020/…
$endgroup$
– Vincent
Aug 18 '14 at 16:47
add a comment |
1 Answer
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there are equation $a^2 (abs(x)-y)^2 + b^2 (abs(x)+y)^2 = 2(ab)^2$
its make love symbol
if ratio $abs(a/b)>1$ :its make the heart
if ratio $abs(a/b)$ too lagre : its make the boomerang
if ratio $abs(a/b) =1$ : its circle
if ratio $abs(a/b) < 1$ : making it upside down
where $a,b$ is in equation $x^2/a^2+y^2/b^2 =1$
edited Jan 10 at 16:49
Armando j18eos
2,63511328
answered Jan 10 at 16:25
vLinh dhvLinh dh
1
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1 Answer
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active
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1 Answer
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active
oldest
votes
active
oldest
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active
oldest
votes
$begingroup$
there are equation $a^2 (abs(x)-y)^2 + b^2 (abs(x)+y)^2 = 2(ab)^2$
its make love symbol
if ratio $abs(a/b)>1$ :its make the heart
if ratio $abs(a/b)$ too lagre : its make the boomerang
if ratio $abs(a/b) =1$ : its circle
if ratio $abs(a/b) < 1$ : making it upside down
where $a,b$ is in equation $x^2/a^2+y^2/b^2 =1$
edited Jan 10 at 16:49
Armando j18eos
2,63511328
answered Jan 10 at 16:25
vLinh dhvLinh dh
1
$endgroup$
add a comment |
$begingroup$
there are equation $a^2 (abs(x)-y)^2 + b^2 (abs(x)+y)^2 = 2(ab)^2$
its make love symbol
if ratio $abs(a/b)>1$ :its make the heart
if ratio $abs(a/b)$ too lagre : its make the boomerang
if ratio $abs(a/b) =1$ : its circle
if ratio $abs(a/b) < 1$ : making it upside down
where $a,b$ is in equation $x^2/a^2+y^2/b^2 =1$
edited Jan 10 at 16:49
Armando j18eos
2,63511328
answered Jan 10 at 16:25
vLinh dhvLinh dh
1
$endgroup$
add a comment |
$begingroup$
there are equation $a^2 (abs(x)-y)^2 + b^2 (abs(x)+y)^2 = 2(ab)^2$
its make love symbol
if ratio $abs(a/b)>1$ :its make the heart
if ratio $abs(a/b)$ too lagre : its make the boomerang
if ratio $abs(a/b) =1$ : its circle
if ratio $abs(a/b) < 1$ : making it upside down
where $a,b$ is in equation $x^2/a^2+y^2/b^2 =1$
edited Jan 10 at 16:49
Armando j18eos
2,63511328
answered Jan 10 at 16:25
vLinh dhvLinh dh
1
$endgroup$
there are equation $a^2 (abs(x)-y)^2 + b^2 (abs(x)+y)^2 = 2(ab)^2$
its make love symbol
if ratio $abs(a/b)>1$ :its make the heart
if ratio $abs(a/b)$ too lagre : its make the boomerang
if ratio $abs(a/b) =1$ : its circle
if ratio $abs(a/b) < 1$ : making it upside down
where $a,b$ is in equation $x^2/a^2+y^2/b^2 =1$
edited Jan 10 at 16:49
Armando j18eos
2,63511328
answered Jan 10 at 16:25
vLinh dhvLinh dh
1
edited Jan 10 at 16:49
Armando j18eos
2,63511328
edited Jan 10 at 16:49
Armando j18eos
2,63511328
edited Jan 10 at 16:49
Armando j18eos
2,63511328
2,63511328
answered Jan 10 at 16:25
vLinh dhvLinh dh
1
answered Jan 10 at 16:25
vLinh dhvLinh dh
1
answered Jan 10 at 16:25
vLinh dhvLinh dh
1
1
add a comment |
add a comment |
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$begingroup$
To help format questions check out the following link. meta.math.stackexchange.com/questions/5020/…
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– Vincent
Aug 18 '14 at 16:47