bio | website | zakuski.math.utsa.edu/~jagy |
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location | Berkeley, California | |
age | 58 | |
visits | member for | 5 years, 2 months |
seen | 2 days ago | |
stats | profile views | 14,880 |
My main activity is in number theory of integral positive ternary quadratic forms. This began through years of working with Irving Kaplansky. Much of his unpublished writing on quadratic forms can be found as pdfs at
http://zakuski.math.utsa.edu/~kap/forms.html
and about Lie and Jordan superalgebras at
http://zakuski.math.utsa.edu/~kap/superalgebra.html
One of my own email addresses can be found easily using the search feature at
http://www.ams.org/cml
and just putting in my last name
Mar 27 |
comment |
Is there a universal straightedge and compass construction of a segment incommensurable to a given one in the hyperbolic plane?
Anyway, in case what you want is to be given an unknown segment and produce something else, how about taking the given length and making that two legs of a right triangle? The hypotenuse can be solved for explicitly. |
Mar 27 |
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Is there a universal straightedge and compass construction of a segment incommensurable to a given one in the hyperbolic plane?
It appears that you do understand that a length $x$ in the hyperbolic plane, take curvature as $-1,$ is constructible if and only if $e^x,$ $\cosh x,$ $\sinh x,$ $\tanh x$ are in the field of lengths constructible in the Euclidean plane. As that does not answer your question, I don't think I can help you at a distance. Commensurability is not a reasonable condition in the hyperbolic plane, there are explicit transcendental functions involved. |
Mar 26 |
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Is there a universal straightedge and compass construction of a segment incommensurable to a given one in the hyperbolic plane?
This is probably why Hartshorne switched to a "multiplicative length" for his (book) axiomatic treatment of the hyperbolic plane. For a length most of us would call $x,$ his multiplicative length is just $e^x,$ which is then in the "constructible field." |
Mar 26 |
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Is there a universal straightedge and compass construction of a segment incommensurable to a given one in the hyperbolic plane?
not sure what you are getting at, but the natural thing to consider is angles, between pairs of lines or two circles that meet or a circle and a line. The fundamental theorem is that the constructible angles in the hyperbolic plane are exactly the same as the constructible angles in the Euclidean plane. |
Mar 18 |
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Homotopy Type Theory: What is it?
Maybe. I believe I was thinking of one of their tiny "what is?" columns, but this will do. I'm just relying on memory here, and not on a topic in which I have any involvement. |
Mar 18 |
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Homotopy Type Theory: What is it?
there have been some popular surveys, including in the AMS Notices I think, available online. |
Mar 7 |
revised |
Averages over integer points of the sphere
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Mar 6 |
revised |
Averages over integer points of the sphere
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Mar 6 |
answered | Averages over integer points of the sphere |
Feb 9 |
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Why is a matrix pencil called a pencil?
"The genus name is derived from the Latin root penicillum, meaning "painter's brush", and refers to the chains of conidia that resemble a broom." en.wikipedia.org/wiki/Penicillium |
Feb 9 |
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Why is a matrix pencil called a pencil?
@KConrad, one example goes back to Appolonius of Perga, no idea what he called it en.wikipedia.org/wiki/Apollonian_circles |
Feb 9 |
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Why is a matrix pencil called a pencil?
suspect it is older than Cayley, used in projective geometry, a pencil of lines, a pencil of points. |
Feb 8 |
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How to approach the stigma of not having a math degree?
Fred E. Katt is not a research mathematician. If you want respect and the benefit of the doubt on career/personal advice on MO, use your real name. |
Feb 6 |
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What do you do if you believe a problem is undecidable?
$$\begin{array}{l}\text{When in danger or in doubt,}\cr \text{Run in circles, scream and shout.}\end{array}$$ |
Feb 6 |
awarded | Nice Answer |
Feb 3 |
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The minimizing problem over a sequence of shrinking balls
math.stackexchange.com/questions/1132206/… |
Jan 27 |
revised |
Parametric solutions of Pell's equation
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Jan 27 |
revised |
Parametric solutions of Pell's equation
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Jan 27 |
revised |
Parametric solutions of Pell's equation
added 143 characters in body |
Jan 27 |
answered | Parametric solutions of Pell's equation |