EREZAVRAHAM.COM

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Erez Avraham Photographer: October 2007

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Wednesday, October 24, 2007. Had a blast this weekend with this great family, I really enjoy taking family portraits outside in a nice park or special place that means a lot to the family. After all, portraits are all about creating memories. I tried to paint this portrait with Corel painter, this is the most complicated software i have. after a few hours of strokes i came up with that. View the video from the session here. Saturday, October 13, 2007. The old website is still alive here.

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Four Points, Two Distances | Affine Mess | Page 7

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January 27, 2009. Four Points, Two Distances. Filed under: Math Circles. 8212; Tags: Math Circles. 8212; Alon Amit @ 10:53 am. The one and only way to arrange five points in the plane so as to form just two distinct distances is by placing them at the vertices of an equilateral pentagon. The last missing solution of our original four-point puzzle is obtained by simply forgetting about one of the five. 7 Comments ». Rhombus with angles 60, 120, 60, 120. 😀. 8212; April 6, 2009 @ 10:35 am. Square = 2 4.

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About | Affine Mess

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Affinemess is mostly about math. I’ll use it for write-ups of talks I’m giving in Math Circles around the SF Bay Area, particularly the San Jose Math Circle. And maybe other math musings I come up with. We’ll see. 8211; A. A. Disclaimer; The views expressed in this blog are my very own and are not endorsed by or representative of my employer, the math circles, or anyone else. Leave a Comment ». Feed for comments on this post. Leave a Reply Cancel reply. Enter your comment here. Address never made public).

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Four Points, Two Distances | Affine Mess | Page 3

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January 27, 2009. Four Points, Two Distances. Filed under: Math Circles. 8212; Tags: Math Circles. 8212; Alon Amit @ 10:53 am. So, how many did you get? Here are five arrangements that you may have stumbled upon. Did you find, or think you’ve found, another one? You may wonder if there are any others… read on to find out! In shape #2, the new point lies directly above the triangle, at a distance of 1 from the top vertex where we assume that 1 is the side length of the equilateral triangle. It also ha...

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Four Points, Two Distances | Affine Mess | Page 6

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January 27, 2009. Four Points, Two Distances. Filed under: Math Circles. 8212; Tags: Math Circles. 8212; Alon Amit @ 10:53 am. Working through most of the others is similar. Whenever there is a red triangle, you know that it must actually be an equilateral triangle in the plane; it is then just a matter of realizing where the fourth point needs to be. In one case there are two options for placing that fourth point – see if you can identify this case. What does it look like? The answer is Yes! There are v...

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Four Points, Two Distances | Affine Mess | Page 5

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January 27, 2009. Four Points, Two Distances. Filed under: Math Circles. 8212; Tags: Math Circles. 8212; Alon Amit @ 10:53 am. The various ways of arranging the coincidences among the six distances are:. Your list may look different but it should be essentially the same. We’ve colored the “points” in gray since they are now not actual points in the plane, just placeholders for describing the length coincidences. 7 Comments ». Rhombus with angles 60, 120, 60, 120. 😀. 8212; April 6, 2009 @ 10:35 am. Your ...

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Four Points, Two Distances | Affine Mess | Page 4

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January 27, 2009. Four Points, Two Distances. Filed under: Math Circles. 8212; Tags: Math Circles. 8212; Alon Amit @ 10:53 am. Fun as it may be to doodle around and stumble upon configurations, at some point we may want to find a more orderly way to approach this problem. Otherwise, how can we ever tell if we’ve indeed covered all the possibilities? 7 Comments ». Rhombus with angles 60, 120, 60, 120. 😀. 8212; April 6, 2009 @ 10:35 am. That’s right. Can you find other ways? Can you find them all? Your #5...

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Four Points, Two Distances | Affine Mess | Page 2

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January 27, 2009. Four Points, Two Distances. Filed under: Math Circles. 8212; Tags: Math Circles. 8212; Alon Amit @ 10:53 am. Here’s the question again:. Apart from the corners of a square, can you find other ways of arranging four points in the plane, such that there are only two distinct distances between them? Go ahead and try scribbling some patterns. Please do not click “Continue” until you’ve come up with at least two new arrangements. 8220; Must I draw only quadrilaterals of various shapes? Well,...

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Four Points, Two Distances | Affine Mess

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January 27, 2009. Four Points, Two Distances. Filed under: Math Circles. 8212; Tags: Math Circles. 8212; Alon Amit @ 10:53 am. Consider four points in the plane, located at the corners of a square:. The points are shown as slightly large circles just so you can see them better. Imagine those are actual points, with no width or height). The first question we’re going to ask is:. Distances between pairs of points are there, in this arrangement? A moment of thought…). Did you get 2? San Jose Math Circle.