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Hello again,
I thought i would mention that i am starting to see a good reason for calling this class of curves "Ovals" even though sometimes they dont look like ovals. That's because the shapes that these equations do generate is based on real ovals that we all know and love, and look somewhat egg shaped. The big difference is we have more than one oval to work with rather than just one, and when the join together they form different overall shapes. But they can be said to originate from actual oval shapes.
I realized this when i did a four point 'oval' (using the word oval for now) that satisfies:
r1*r2*r3*r4=K
This is actually four ovals that may or may not be joined (see attachment).
In the attachment, we can see the morph between the larger lobe and two smaller lobes. Changing K a little more will mean the two smaller ovals split completely from the larger oval and so we get three separate ovals. going farther with K, that larger oval will split into two also and so we will end up with four ovals.
Going in the other direction with K, the four will join to make one large oval.
So even though that picture does not look like a traditional oval, it might be ok to call it such, or maybe at least mention that it comes from ovals that are joined together to form one single shape.
You be the judge
This next graph is a four point 'oval' with two constant points on the x axis and two not on any axis. Ignore artifacts.
Pretty interesting i think.
I thought i would mention that i am starting to see a good reason for calling this class of curves "Ovals" even though sometimes they dont look like ovals. That's because the shapes that these equations do generate is based on real ovals that we all know and love, and look somewhat egg shaped. The big difference is we have more than one oval to work with rather than just one, and when the join together they form different overall shapes. But they can be said to originate from actual oval shapes.
I realized this when i did a four point 'oval' (using the word oval for now) that satisfies:
r1*r2*r3*r4=K
This is actually four ovals that may or may not be joined (see attachment).
In the attachment, we can see the morph between the larger lobe and two smaller lobes. Changing K a little more will mean the two smaller ovals split completely from the larger oval and so we get three separate ovals. going farther with K, that larger oval will split into two also and so we will end up with four ovals.
Going in the other direction with K, the four will join to make one large oval.
So even though that picture does not look like a traditional oval, it might be ok to call it such, or maybe at least mention that it comes from ovals that are joined together to form one single shape.
You be the judge
This next graph is a four point 'oval' with two constant points on the x axis and two not on any axis. Ignore artifacts.
Pretty interesting i think.
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