- #1
Gringo22
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Edit in new post. Or Bumping with the edited change.
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What Makes a Vertex Dynamic in Shape Diversity?
- Thread starter Gringo22
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- fermat's theorem Theorem
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Discussion Overview
The discussion revolves around the concept of a "dynamic vertex" in the context of the equation A² + B² = C², exploring its implications for shape diversity and mathematical representation. Participants engage with philosophical ideas and mathematical interpretations, particularly relating to Fermat's theorem and the nature of vertices in geometric shapes.
Discussion Character
- Exploratory
- Conceptual clarification
- Debate/contested
Main Points Raised
- One participant proposes that a dynamic vertex in the equation A² + B² = C² could explain variations in shape, suggesting that each instance of a "curl" at this vertex results in a unique shape.
- Another participant questions the meaning of "dynamic vertex" and its relevance to the equation, expressing confusion about its connection to Fermat's theorem.
- A later reply attempts to clarify that a dynamic vertex is one that bends to form the angle between two lines, leading to diversity in shapes when similar forms interact at this vertex.
- Some participants express frustration over the lack of clarity regarding the concept of a dynamic vertex, indicating that it remains poorly understood within the discussion.
Areas of Agreement / Disagreement
Participants do not reach a consensus on the definition or implications of a dynamic vertex, with multiple interpretations and significant confusion expressed throughout the thread.
Contextual Notes
There are unresolved assumptions regarding the mathematical and philosophical implications of a dynamic vertex, as well as its connection to established mathematical theorems.
- #2
Gringo22
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If I postulate there is 1 dynamic vertex in A2+B2=C2.
What would this look like mathematically, and what would this prove ?
I'm thinking the vertex explains a curl. AND if it's dynamic it explains why Fermat thought it explained exerything. Because no two curlings on this dynamic vertex are the same. For proof, you can't make a fist and have it be the same shape as it was the first time. Each time the curl of the fist is new. So if you kept making fists you would run into infinity with a new shape every time, thus proving that very point.
What would this look like mathematically, and what would this prove ?
I'm thinking the vertex explains a curl. AND if it's dynamic it explains why Fermat thought it explained exerything. Because no two curlings on this dynamic vertex are the same. For proof, you can't make a fist and have it be the same shape as it was the first time. Each time the curl of the fist is new. So if you kept making fists you would run into infinity with a new shape every time, thus proving that very point.
- #3
HallsofIvy
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I have absolutely no idea what this means. I assume that you mean A2+ B2= C2 but I don't know what you mean by a "dynamic vertex" or how anything called a "vertex" or that is "dynamic" could be in an equation.
Do you even know what Fermat's (last) theorem says? It has nothing to do with A2+ B2= C2.
Do you even know what Fermat's (last) theorem says? It has nothing to do with A2+ B2= C2.
- #4
Gringo22
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HallsofIvy said:
Ah. My ignorance is showing through.
I'll repeat my question.
In the Triangle A2+ B2= C2
What if one of the 3 angles is a dynamic vertex, joining two lines on the triangle.
Every time these three points are created, they are different.
This is to show a philosophical concept "Monkey see Monkey do."
The Monkey tries to plug the sea by sticking in his finger.
- #5
matt grime
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and no one is any the wiser as to what a dynamic vertex is...
- #6
HallsofIvy
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Every vertex joins two lines on a triangle. What is a "dynamic vertex"?
- #7
Gringo22
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matt grime said:
Ah, I see ! I'm sorry.
A dynamic vertex is a vertex that bends to form the curl/angle of the two lines joined to it. This shape shows me that when two similar shapes in real life curl/angle at a vertex they are different. So It dawned on me that this is because the vertex joining the two lines is dynamic.
That's why there's diversity. When similar shapes bend at the vertex, they bend slightly different.
The various diversities are what I'm thinking about now.
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