Math 350 Section 2.1 Answers to Classwork
... outer sides line up to form a square. The region inside the arrangement is a rhombus since all its sides are of length c 1. Recall that the sum of the angles in a triangle is always 180 degrees. Why does this guarantee that the angles of the inner quadrilateral are right angles? Why does this mean t ...
... outer sides line up to form a square. The region inside the arrangement is a rhombus since all its sides are of length c 1. Recall that the sum of the angles in a triangle is always 180 degrees. Why does this guarantee that the angles of the inner quadrilateral are right angles? Why does this mean t ...
Solution
... assume a′m > b′m . Consider the numbers a′m , a′m+1 , . . . , a′n and b′1 , b′2 , . . . , b′m . As there are n + 1 numbers altogether and only n places in the initial sequence there must exist an index j such that we have aj among a′m , a′m+1 , . . . , a′n and bj among b′1 , b′2 , . . . , b′m . Now, ...
... assume a′m > b′m . Consider the numbers a′m , a′m+1 , . . . , a′n and b′1 , b′2 , . . . , b′m . As there are n + 1 numbers altogether and only n places in the initial sequence there must exist an index j such that we have aj among a′m , a′m+1 , . . . , a′n and bj among b′1 , b′2 , . . . , b′m . Now, ...
4.2 Tilings INSTRUCTOR NOTES
... NOTE: The sum of the interior angles surrounding a vertex in any tiling must add up to 360°. In a regular tiling all of the angle measures must be the same. So the “number of polygons” surrounding a vertex times the measure of the same angle must equal 360°. In general for a regular tiling, (number ...
... NOTE: The sum of the interior angles surrounding a vertex in any tiling must add up to 360°. In a regular tiling all of the angle measures must be the same. So the “number of polygons” surrounding a vertex times the measure of the same angle must equal 360°. In general for a regular tiling, (number ...
