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Stanley Rabinowitz

Stanley Rabinowitz
MathPro Press

PhD

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66
Publications
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292
Citations

Publications

Publications (66)
Preprint
Full-text available
The diagonals of a quadrilateral form four component triangles (in two ways). For each of various shaped quadrilaterals, we examine 1000 triangle centers located in these four component triangles. Using a computer, we determine when the four centers form a special quadrilateral, such as a rhombus or a cyclic quadrilateral. A typical result is the f...
Preprint
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The first isodynamic point of a triangle is one of many notable points associated with a triangle. It is named X(15) in the Encyclopedia of Triangle Centers. This paper surveys known results about this point and gives additional properties that were discovered by computer.
Preprint
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The incircle of a triangle touches the sides of the triangle in three points. It is well known that the lines from these points to the opposite vertices meet at a point known as the Gergonne point of the triangle. We use a computer to discover and catalog properties of the Gergonne point.
Article
Full-text available
We use a computer to determine the relative location of Kimberling centers X(1) through X(100) with respect to the incircle of a triangle. For example, for all triangles, we determine which centers must lie inside the incircle and which must lie outside the incircle. We also present inequalities representing how far away these centers can get from...
Article
Full-text available
The first isodynamic point of a triangle is one of many notable points associated with a triangle. It is named X(15) in the Encyclopedia of Triangle Centers. This paper surveys known results about this point and gives additional properties that were discovered by computer.
Article
Full-text available
A cevian is a line segment joining the vertex of a triangle and a point on the opposite side. Well-known cevians are medians, angle bisectors, and altitudes. We consider various cevians passing through named triangle centers such as the Gergonne point and Nagel point. We show how a computer can be used to discover, not just prove, identities involv...
Article
Full-text available
A Gergonne cevian is the cevian through the Gergonne point of a triangle. A Nagel cevian is the cevian through the Nagel point of a triangle. We present some new inequalities involving the lengths of the Gergonne and Nagel cevians of a triangle. Mathematica was used to both discover and prove some of these results.
Preprint
Full-text available
If P is a point inside triangle ABC, then the cevians through P extended to the circumcircle of triangle ABC create a figure containing a number of curvilinear triangles. Each curvilinear triangle is bounded by an arc of the circumcircle and two line segments lying along the sides or cevians of the original triangle. We give theorems about the rela...
Preprint
Full-text available
We systematically investigate properties of various triangle centers (such as orthocenter or incenter) located on the four faces of a tetrahedron. For each of six types of tetrahedra, we examine over 100 centers located on the four faces of the tetrahedron. Using a computer, we determine when any of 16 conditions occur (such as the four centers bei...
Article
Full-text available
We systematically investigate properties of various triangle centers (such as orthocenter or incenter) located on the four faces of a tetrahedron. For each of six types of tetrahedra, we examine over 100 centers located on the four faces of the tetrahedron. Using a computer, we determine when any of 16 conditions occur (such as the four centers bei...
Article
Full-text available
If P is a point inside ABC, then the cevians through P divide ABC into six small triangles. We give theorems about the relationships between the areas of these triangles.
Article
Full-text available
If P is a point inside triangle ABC, then the cevians through P extended to the circumcircle of triangle ABC create a figure containing a number of curvilinear triangles. Each curvilinear triangle is bounded by an arc of the circumcircle and two line segments lying along the sides or cevians of the original triangle. We give theorems about the rela...
Article
Full-text available
If P is a point inside triangle ABC, then the cevians through P divide triangle ABC into smaller triangles of various sizes. We give theorems about the relationships between the radii of various circles associated with these triangles.
Preprint
Full-text available
If P is a point inside triangle ABC, then the cevians through P divide triangle ABC into smaller triangles of various sizes. We give theorems about the relationships between the radii of various circles associated with these triangles.
Article
Full-text available
If P is a point inside triangle ABC, then the cevians through P divide triangle ABC into six small triangles. We give theorems about the relationships between the radii of the circumcircles of these triangles. We also state some results about the relationships between the circumcenters of these triangles.
Preprint
Full-text available
If P is a point inside triangle ABC, then the cevians through P extended to the circumcircle of triangle ABC create a figure containing a number of curvilinear triangles. Each curvilinear triangle is bounded by an arc of the circumcircle and two line segments lying along the sides or cevians of the original triangle. We give theorems about the rela...
Preprint
Full-text available
If P is a point inside triangle ABC, then the cevians through P divide triangle ABC into six small triangles. We give theorems about the relationship between the radii of the circles inscribed in these triangles and the lengths of the segments formed along the sides of the triangle.
Preprint
Full-text available
If P is a point inside triangle ABC, then the cevians through P divide triangle ABC into smaller triangles of various sizes. We give theorems about the relationship between the radii of certain excircles of some of these triangles.
Preprint
Full-text available
If P is a point inside triangle ABC, then the cevians through P divide triangle ABC into small triangles. We give theorems about the relationship between the radii of the circumcircles of these triangles.
Preprint
Full-text available
If P is a point inside triangle ABC, then the cevians through P divide triangle ABC into six smaller triangles. We give theorems about the relationship between the radii of the circles inscribed in these triangles.
Preprint
If P is a point inside triangle ABC, then the cevians through P divide triangle ABC into six smaller triangles. We give theorems about the relationship between the radii of the circles inscribed in these triangles.
Experiment Findings
Full-text available
Let P be a point inside triangle ABC. The cevians through P divide triangle ABC into 6 smaller triangles. Consider the incircles of these 6 triangles. I am investigating the relationship between the radii of the 6 incircles. There must be some relationship between these six radii, but I have not found a general formula yet. Here are some particul...
Article
Full-text available
If P is a point inside triangle ABC, then the cevians through P divide triangle ABC into smaller triangles of various sizes. We give theorems about the relationship between the radii of certain excircles of some of these triangles.
Article
Full-text available
If P is a point inside triangle ABC, then the cevians through P divide triangle ABC into six small triangles. We give theorems about the relationship between the radii of the circles inscribed in these triangles and the lengths of the segments formed along the sides of the triangle.
Chapter
Full-text available
Paper 13: Stanley Rabinowitz and Stan Wagon, “A spigot algorithm for the digits of π,” American Mathematical Monthly, vol. 102 (March 1995), p. 195–203. Copyright 1995 Mathematical Association of America. All Rights Reserved. Synopsis: In this paper, Rabinowitz and Wagon introduce a very interesting “spigot algorithm” for the digits of π. In partic...
Patent
Full-text available
In one general aspect, a data access method is disclosed that includes directing data block write requests from different clients to different data storage servers based on a map. Data blocks referenced in the data block write requests are stored in the data storage servers. Data from the data write requests are also relayed to a parity server, and...
Article
Full-text available
Am odel is described and analyzed for a multiprocessor shared memory system in which each memory bank can service a fixed number of access requests per cpu cycle. If n processors simultaneously request data from a common shared memory, it is usually not possible for all the requests to be satisfied at the same time. This is because the memory syste...
Article
Full-text available
Some Bonnesen-style isoperimetric inequalities for triangles in the plane are presented. For example, it is shown that L 2 -12√3A ≥ 35.098 r(R -2r) for triangles with perimeter L, area A, inradius r, and circumradius R. Equality holds when and only when either the triangle is equilateral or the triangle is similar to the isosceles triangle with sid...
Book
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Mathematical journal and contest problems from 1975-1979 arranged by subject. Includes author index.
Article
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Algorithms for evaluating or simplifying sums of the form $$\sum_{n=1}^{N}\frac{1}{F_{n+a_1}F_{n+a_2} \cdots F_{n+a_r}}$$ where the F i are Fibonacci numbers and the a i, are integers have been discussed in [13]. It is the goal of this paper to generalize these results to arbitrary second-order linear recurrences.
Article
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Article
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Methods for manipulating trigonometric expressions, such as changing sums to products, changing products to sums, expanding functions of multiple angles, etc., are well-known [1], In fact, the process of verifying trigonometric identities is algorithmic (see [2] or [5]). Roughly speaking, all trigonometric identities can be derived from the basic i...
Conference Paper
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This paper deals with linear systems of difference equations whose coefficients admit generalized factorial series representations at z = ∞. We shall give a criterion by which a given system is determined to have a regular singularity. In the same ...
Article
Full-text available
Given a convex lattice polygon with g interior lattice points, we find upper and lower bounds for the perimeter, diameter, and width of the polygon. For small g, the extremal figures were found by computer. A lattice point in the plane is a point with integer coordinates. The set of all lattice points in the plane is denoted by Z2 .A lattice polygo...
Article
Let S b ea set of mn +1 lattice points in En. Then either some two points of S span a hole (have a lattice point not in S between them), or some m +1 points of S are collinear.

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Projects

Projects (3)
Project
Discover new geometry results using a computer.
Project
Let P be a point inside triangle ABC. The cevians through P divide triangle ABC into 6 smaller triangles. Consider the incircles of these 6 triangles. I am investigating the relationship between the radii of the 6 incircles.
Project
Determine ways to use computers to automatically prove identities involving Fibonacci numbers and numbers from other recurrences.