maltitudes of a quadrilateral are concurrent

For any quadrilateral one can define the so-called maltitudes. A maltitude on a side of a quadrilateral is defined as the line through the midpoint of the side and perpendicular to the opposite side. Generally the four maltitudes of a quadrilateral are not concurrent, but if the quadrilateral is cyclic they are. Prove that indeed the maltitudes of any cyclic quadrilateral ABCD are concurrent and that their point of concurrency is the reflection of the circumcenter of ABCD in the center point of ABCD. The circumcircle to ABCD is obtained by drawing lines through the midpoints of the sides and perpendicular to the sides themselves. Look for parallelograms and keep in mind that the di... click for more

Understanding Wave diagrams?

Hi, I am having a bit of trouble understanding a so called "wave diagram". I am reading the book "The Power of Limits" by Gyorgy Doczi, which is about the relationship of shape, music, nature etc to the goldern section. A lot of the book has diagrams relating to an object showing how the forms relate to the goldern section. One such diagram is a wave diagram, and connects a dinergic diagram and a diagram of the object, to create a wave diagram which represents the object. I dont understand how the wave diagram was created, or what it entirely means? I have attached two images which show the wave diagrams. The first image, the wave diagrams are on the far right and left. The second is... click for more

vector functions of one variable

see attached

vector functions of one variable

see attached.

vector functions of one variable

see attahced