Clark Kimberling Video
matematico, professore universitario
- flauto dolce
- Stati Uniti d'America
Ultimo aggiornamento
2024-05-10
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The isogonal (or isotomic) conjugate of a line with respect to a triangle is a circumconic [1]. If an elliptic billiard is regarded as a stationary, X(9)-centered circumellipse to the 3-periodic family, we can analyze its isogonal and isotomic conjugate lines dynamically. These turn out to be [3] the orbits' Antiorthic Axis [4] and Line L(31) [5], respectively. In particular, what is the envelope [2] of such straight lines over the family of 3-periodics? The two lines can be constructed with any pair of Triangle Centers lying on them (Peter Moses provides many in [3]). For special reasons, we use: a) L(1), Antiorthic Axis, X(44)X(513) b) L(31), Line X(514)X(661) / note: to be reviewed, but this is the Gergonne line of a triangle derived from the reference one. ACT? The video shows the locus of the above Triangle Centers for an a/b=1.618=phi billiard, drawn black. Orbits are drawn blue, as well as the envelope of said lines. Specifically: Left: the non-elliptic locus of X(44) is shown red. The elliptic locus of X(1155) is shown green. Notice how the Antiorthic axis (dashed blue) is dynamically tangent to the latter, i.e., the locus of X(1155) is the envelope of the Antiorthic Axis. Right: the non-elliptic locus of X(857) which lies on L(31) is shown red. The elliptic locus of X(908), also on L(31), is shown green. Notice how line L(31) (dashed blue) is dynamically tangent to the latter, i.e., the locus of X(908) is the envelop of L(31). In both cases, "C" depicts where the envelope currently is. [1] (http•••) [2] (http•••) [3] Peter Moses, mentioed by Clark Kimberling, ETC under X(9), (http•••) [4] (http•••) [5] (http•••)
A Christmas serenade from our front step, where we've been regularly making music since the start of the pandemic. These fun, creative, challenging arrangements by Clark Kimberling are new to us this year. Mr. Kimberling intended for these to be played on solo soprano recorder or flute, but I think they work fine for violin as well (we may try playing them on recorder in the future).
Clark Kimberling's remarkable Encyclopedia of Triangle Centers is a fabulous resource for geometers! Here is the link to it: (http•••)/ Screenshot PDFs for my videos are available at the website (http•••). These give you a concise overview of the contents of the lectures for various Playlists: great for review, study and summary. My research papers can be found at my Research Gate page, at (http•••) My blog is at (http•••) where I will discuss lots of foundational issues, along with other things. Online courses will be developed at openlearning.com. The first one, already underway is Algebraic Calculus One at (http•••) Please join us for an exciting new approach to one of mathematics' most important subjects! If you would like to support these new initiatives for mathematics education and research, please consider becoming a Patron of this Channel at (http•••) Your support would be much appreciated.
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- cronologia: Compositori (Nord America).
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