User talk:Wanderer909

April 2024[edit]

Hello, I'm MrOllie. I noticed that you made a comment that didn't seem very civil, so it may have been removed. Wikipedia is built on collaboration, so it's one of our core principles to interact with one another in a polite and respectful manner. If you have any questions, you can leave me a message on my talk page. Thank you. MrOllie (talk) 20:41, 8 April 2024 (UTC)[reply]

Kindly go through the following section and take opinions of any leading mathematician or Number Theorist across the globe whether or not the following is the most important aspect of Metallic Ratios or not :

==Relation to Pythagorean triples==

Metallic Ratios in Primitive Pythagorean Triangles

Metallic means are precisely represented by primitive Pythagorean triples.

In a primitive Pythagorean triple, if the difference between hypotenuse and longer leg is 1, 2 or 8, such Pythagorean triple accurately represents one particular metallic mean. The cotangent of the quarter of smaller acute angle of such Pythagorean triangle equals the precise value of one particular metallic mean.

Consider a primitive Pythagorean triple (a,b,c) in which a < b < c and c - b ∈ {1, 2, 8}. Such Pythagorean triangle (a,b,c) yields the precise value of a particular metallic mean

S_{m}

as follows :

S_{m}=cot\left({\frac {\theta }{4}}\right)

where θ is the smaller acute angle of the Pythagorean triangle

and

m=2{\sqrt {\frac {c+b}{c-b}}}

For example, the primitive Pythagorean triple 20-21-29 incorporates the 5th metallic mean. Cotangent of the quarter of smaller acute angle of the 20-21-29 Pythagorean triangle yields the precise value of the 5th metallic mean.

Similarly, the Pythagorean triangle 3-4-5 represents the 6th metallic mean.

Likewise, the Pythagorean triple 12-35-37 gives the 12th metallic mean, the Pythagorean triple 52-165-173 yields the 13th metallic mean, and so on.

^[1] Wanderer909 (talk) 21:28, 8 April 2024 (UTC)[reply]

Please refrain from making unconstructive edits to Wikipedia. Your edits appear to be disruptive and have been or will be reverted.

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Please ensure you are familiar with Wikipedia's policies and guidelines, and please do not continue to make edits that appear disruptive. Continued disruptive editing may result in loss of editing privileges. Thank you. MrOllie (talk) 20:56, 8 April 2024 (UTC)[reply]

You may be blocked from editing without further warning the next time you disrupt Wikipedia. MrOllie (talk) 20:58, 8 April 2024 (UTC)[reply]

You have been blocked indefinitely from editing for persistently making disruptive edits.

If you think there are good reasons for being unblocked, please review Wikipedia's guide to appealing blocks, then add the following text to the bottom of your talk page: {{unblock|reason=Your reason here ~~~~}}. Widr (talk) 12:37, 9 April 2024 (UTC)[reply]

^ Rajput, Chetansing; Manjunath, Hariprasad (2024). "Metallic means and Pythagorean triples | Notes on Number Theory and Discrete Mathematics". Bulgarian Academy of Sciences.{{cite web}}: CS1 maint: numeric names: authors list (link)

[1] Rajput, Chetansing; Manjunath, Hariprasad (2024). "Metallic means and Pythagorean triples | Notes on Number Theory and Discrete Mathematics". Bulgarian Academy of Sciences.{{cite web}}: CS1 maint: numeric names: authors list (link)

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