# 99 Points of Intersection: Examples, Pictures, Proofs by Hans Walser

By Hans Walser

The ninety nine issues of intersection offered the following have been amassed in the course of a year-long look for astonishing concurrence of traces. for every instance we discover compelling facts for the occasionally startling incontrovertible fact that in a geometrical determine 3 immediately traces, or occasionally circles, go through one and a similar aspect. in fact, we're acquainted with a few examples of this from easy straightforward geometry - the intersection of medians, altitudes, attitude bisectors, and perpendicular bisectors of facets of a triangle. right here there are various extra examples - a few for figures except triangles, a few the place much more than 3 directly traces go through a standard point.The major a part of the e-book offers ninety nine issues of intersection simply visually. they're constructed in a series of figures, many with no caption or verbal statement. additionally the publication includes normal techniques on and examples of the issues of intersection, in addition to a few normal tools of proving their life. a few of the examples proven within the booklet have been encouraged through questions and recommendations made via scholars and high-school academics. a number of of these examples haven't just a geometrical, but additionally an fascinating aesthetic, aspect.The publication addresses high-school scholars and scholars on the undergraduate point in addition to their lecturers, yet will entice somebody attracted to geometry

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Extra info for 99 Points of Intersection: Examples, Pictures, Proofs

Example text

At the beginning of month 2 we have the original pair PI and its first pair of offspring, Pl' At the beginning of month 3 we have the original pair PI, its first pair of offspring P2 born at the beginning of month 2, and its second pair of offspring, P3 . At the beginning of month 4 we have PI , P2 , and P3 ; P" , the offspring of PI; and P5 , the offspring of P2 . Let II " denote Ihe number of pairs of rabbits at the beginning of month II . We see Ihat The sequence expands rapidly, and we gel I.

L~l i= c. • We summarize some of the differences between matrix multiplication and the multiplication of real numbers as follows: For matrices A, B. and C of the appropriate sizes, I. AB need not equal BA. 2. A B may be the zero matrix with A 3. AB may equal AC with B c. t- 0 and B t- O. t- In this sectio n wc have developed a number of pro perties about matrices and their transposes. If a future problem involves these concepts, refer to these pro perties to help solve the problem. These results can be used to develop many more results .

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