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edited Feb 23, 2011 at 0:48

Horn angles and variations thereof appear to be well studied in conformal geometry, see e.g. the papers by Ladue, Mary Elizabeth "Conformal geometry of horn angles of higher order", Amer. J. Math. 65, (1943), 455–476, and "Trihornometry: A New Chapter of Conformal Geometry" by Edward Kasner, Proceedings of the National Academy of Sciences of the United States of America, Vol. 23, No. 6 (Jun. 15, 1937), pp. 337-341
You can find more about themthe theory of horn angles in the paper "The recent theory of the horn angle" by E. Kasner, Scripta Math. 11, (1945). 263–267, 53.0X. It The paper is from 1945, but it should give you some idea about the directions of study in that area.
HornYour intuition is right as horn angles can be measured within the model of superreal numbers (in the sense of D. O. Tall), see the paper by J. Bair and V. Henry "Angles corniculaires et nombres superréels" (French) ("Horn angles and superreal numbers), Bull. Belg. Math. Soc. Simon Stevin 15 (2008), no. 1, 77–86.

Horn angles and variations thereof appear to be well studied in conformal geometry, see e.g. the papers by Ladue, Mary Elizabeth "Conformal geometry of horn angles of higher order", Amer. J. Math. 65, (1943), 455–476, and "Trihornometry: A New Chapter of Conformal Geometry" by Edward Kasner, Proceedings of the National Academy of Sciences of the United States of America, Vol. 23, No. 6 (Jun. 15, 1937), pp. 337-341
You can find more about them in the paper "The recent theory of the horn angle" by E. Kasner, Scripta Math. 11, (1945). 263–267, 53.0X. It is from 1945, but it should give you some idea about the directions of study in that area.
Horn angles can be measured within the model of superreal numbers, see the paper by J. Bair and V. Henry "Angles corniculaires et nombres superréels" (French) ("Horn angles and superreal numbers), Bull. Belg. Math. Soc. Simon Stevin 15 (2008), no. 1, 77–86.

Horn angles and variations thereof appear to be well studied in conformal geometry, see e.g. the papers by Ladue, Mary Elizabeth "Conformal geometry of horn angles of higher order", Amer. J. Math. 65, (1943), 455–476, and "Trihornometry: A New Chapter of Conformal Geometry" by Edward Kasner, Proceedings of the National Academy of Sciences of the United States of America, Vol. 23, No. 6 (Jun. 15, 1937), pp. 337-341
You can find more about the theory of horn angles in the paper "The recent theory of the horn angle" by E. Kasner, Scripta Math. 11, (1945). 263–267, 53.0X. The paper is from 1945, but it should give you some idea about the directions of study in that area.
Your intuition is right as horn angles can be measured within the model of superreal numbers (in the sense of D. O. Tall), see the paper by J. Bair and V. Henry "Angles corniculaires et nombres superréels" (French) ("Horn angles and superreal numbers), Bull. Belg. Math. Soc. Simon Stevin 15 (2008), no. 1, 77–86.

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created Feb 22, 2011 at 22:03

Horn angles and variations thereof appear to be well studied in conformal geometry, see e.g. the papers by Ladue, Mary Elizabeth "Conformal geometry of horn angles of higher order", Amer. J. Math. 65, (1943), 455–476, and "Trihornometry: A New Chapter of Conformal Geometry" by Edward Kasner, Proceedings of the National Academy of Sciences of the United States of America, Vol. 23, No. 6 (Jun. 15, 1937), pp. 337-341
You can find more about them in the paper "The recent theory of the horn angle" by E. Kasner, Scripta Math. 11, (1945). 263–267, 53.0X. It is from 1945, but it should give you some idea about the directions of study in that area.
Horn angles can be measured within the model of superreal numbers, see the paper by J. Bair and V. Henry "Angles corniculaires et nombres superréels" (French) ("Horn angles and superreal numbers), Bull. Belg. Math. Soc. Simon Stevin 15 (2008), no. 1, 77–86.