Geometric Wonders on GeoGebra Tube

In 1924, Frank Morley published the theorem which stated:"The adjacent angle trisectors of any triangle intersect

at three points determining an equilateral triangle"

Quadrilateral formed by joining the midpoints of sides of any quadrilateral is always a parallelogram.Select the check-box for diagonals of the original quadrilateral, drag the vertices and observe the condition on the diagonals for the parallelogram to be rectangle, rhombus or square.

"In any triangle,the mid points of the sides, the feet of the altitudes, and the midpoint of the segments from the orthocentre to the vertices lie on a circle."

In 1765,Leonhard Euler showed that six of these points,the midpoints of the sides and feet of the altitudes define a unique circle.Yet not until 1820, when a paper published by Brianchon and Poncelet appeared , were the remaining three points found to be on this circle.

String art has its origins in the 'curve stitch' activities invented by Mary Everest Boole at the end of the 19th Century to make mathematical ideas more accessible to children.It was popularised as a decorative craft in the late 1960s through kits and books.

Thread, wire, or string is wound around a grid of nails hammered into a velvet-covered wooden board. Though straight lines are formed by the string, the slightly different angles and metric positions at which strings intersect may give the appearance of Bézier curves (and often construct actual quadratic Bézier curves).

In the 18th century, the Swiss mathematician Leonhard Euler noticed that three of the many centers of a triangle are always collinear, that is, they always lie on a straight line. This line has come to be named after him - the Euler line. The three centers that have this surprising property are the triangle's centroid , circumcenter and orthocenter.