first task - die erste Aufgabe
Two square tablecloths are to be made into one large square tablecloth with the same area.
Find a square that has the same total area as two given squares.
Can you do this for two different squares? - Kann man dies mit zwei unterschiedlichen Quadraten erreichen?
applications - Anwendungen
- find the length of the hypotenuse
- find the length of a cathetus (one of the legs) in a right-angled triangle
- find the distance between two points in a cartesian coordinate system
- construct a right angle (rope with knots) on a field
- verify if a triangle is right-angled
- construct roots
- construct rectangles with the same area as a given square
- problems like this:
In a pond, five feet from the shore, one foot of a reed is visible above the water. If you pull the reed towards the shore, the tip just touches the shore. How deep is the pond?
Another task. The base line is the tangent to the 2 large circle sectors and the small inscribed circle. Show that the radius of the small circle is a fourth of the radius of the two larger circles.
Beweise, dass der Radius des kleineren Kreises genau ein viertel des Radiuses der beiden größeren Kreise ist.