Point-Line Ellipses and Hyperbolas

نویسندگان

چکیده

The author alters the definitions of ellipses and hyperbolas by using a line point not on as foci, instead two points. He develops resulting prototypical diagrams from both synthetic analytic perspectives, well making use technology.

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Minimal Enclosing Hyperbolas of Line Sets

We prove the following theorem: If H is a slim hyperbola that contains a closed set S of lines in the Euclidean plane, there exists exactly one hyperbola Hmin of minimal volume that contains S and is contained in H. The precise concepts of “slim”, the “volume of a hyperbola” and “straight lines or hyperbolas being contained in a hyperbola” are defined in the text.

متن کامل

Finding Ellipses and Hyperbolas Tangent to Two, Three, or Four given Lines

Given lines Lj , j = 1, 2, 3, 4, in the plane, such that no three of the lines are parallel or are concurrent, we want to find the locus of centers of ellipses tangent to the Lj . In the case when the lines form the boundary of a four sided convex polygon R, let M1 and M2 be the midpoints of the diagonals of R. Let L be the line thru M1 and M2, let Z be the open line segment connecting M1 and M...

متن کامل

Ellipses, near Ellipses, and Harmonic Möbius Transformations

It is shown that an analytic function taking circles to ellipses must be a Möbius transformation. It then follows that a harmonic mapping taking circles to ellipses is a harmonic Möbius transformation. Analytic Möbius transformations take circles to circles. This is their most basic, most celebrated geometric property. We add the adjective ‘analytic’ because in a previous paper [1] we introduce...

متن کامل

The Touchpoints Triangles and the Feuerbach Hyperbolas

In this paper we generalize the famous Kariya theorem on the perspectivity of a given triangle with the homothetic images of the intouch triangle from the incenter to the touchpoints triangles of the excircles, leading to the triad of ex-Feuerbach hyperbolas. We also study in some details the triangle formed by the orthocenters of the touchpoints triangles. An elegant construction is given for ...

متن کامل

Ellipses and Lambda Definability

Ellipses are a meta-linguistic notation for denoting terms the size of which are specified by a meta-variable that ranges over the natural numbers. In this work, we present a systematic approach for encoding such meta-expressions in the λ-calculus, without ellipses: Terms that are parameterized by meta-variables are replaced with corresponding λ-abstractions over actual variables. We call such ...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Mathematics Teacher: Learning and Teaching PK–12

سال: 2023

ISSN: ['2330-0582', '0025-5769']

DOI: https://doi.org/10.5951/mtlt.2022.0229