The Volume Common to Two Congruent Circular Cones whose Axes Intersect Symmetrically
نویسندگان
چکیده
In this paper we find the volume of the intersection of two congruent circular cones whose axes cross at a common point P , with the vertices of the cones equidistant from P . The formula is expressible by elementary functions. The symbol manipulator MACSYMA was used in the derivations. The formula was needed for a practical application. It has not been found in the literature despite a thorough search.
منابع مشابه
Penumbra Measurements and Comparison of In-House and Standard Circular Cones by the Gafchoromic Film, Pinpoint Ion Chamber, and MCNPX Monte Carlo Simulation
Introduction: Penumbra is an important property of the radiation beam to obtain a suitable margin surrounding the target volume. Therefore, the precise penumbra width determination in stereotactic radiotherapy is necessary for treatment planning. This study aimed to compare the obtained results of penumbra width by in-house and standard circul...
متن کاملGeometry of orientation and ocular dominance columns in monkey striate cortex.
In addition to showing that ocular dominance is organized in slabs and that orientation preferences are organized in linear sequences likely to reflect slabs, Hubel and Wiesel (1974a) discussed the intriguing possibility that slabs of orientation might intersect slabs of ocular dominance at some consistent angle. Advances in optical imaging now make it possible to test this possibility directly...
متن کاملOptical Möbius Strips in Three Dimensional Ellipse Fields: Lines of Circular Polarization
The major and minor axes of the polarization ellipses that surround singular lines of circular polarization in three dimensional optical ellipse fields are shown to be organized into Möbius strips. These strips can have either one or three half-twists, and can be either right-or left-handed. The normals to the surrounding ellipses generate cone-like structures. Two special projections, one new ...
متن کاملSeparability of Polyhedra and a New Approach to Spatial Storage (Extended Abstract)
EEcient storage and access methods for large amounts of spatial objects are key issues in Geographic Information Systems (GIS), Computer Aided Design (CAD), VLSI design and also Linear Constraint Databases (LCDBs) BJM92], a new application domain in which objects are convex multidimensional polyhedra represented as conjunctions of linear constraints over real variables. Typically, the rst step ...
متن کاملWelfare versus market access: The implications of tariff structure for tariff reform
We show that the effects of tariff changes on welfare and import volume are fully characterised by their effects on the generalised mean and variance of the tariff distribution, implying two "cones of liberalisation" in commodity price space. Because welfare is negatively but import volume positively related to the generalised variance, the cones do not intersect, which poses a policy dilemma. ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- J. Symb. Comput.
دوره 4 شماره
صفحات -
تاریخ انتشار 1987