#### Cynthia Lanius Thanks to PBS for permission to use the Pyramid photo.

# Hidden Irrationals

On the dot paper below, the horizontal and vertical distance from one dot to the other is 1 unit. Draw line segments with the following lengths and label with their lengths.

You may explore on an interactive geoboard here. (A new window will open so that you can go back and forth from the two pages if you like.)

 1. square root 2 2. square root 5 3. square root 8 4. square root 18 5. square root 20 6. square root 26 7. square root 32 8. square root 34 9. square root 40
 10. Choose 3 other lengths of irrational numbers that you can draw by connecting dots. Draw and label. 11. Give 3 other irrational-number lengths that you can not draw connecting dot to dot. 12. Explain what has to be true for you to be able to draw the number lengths in this way. 13. Are all the diagonals irrational? Convince me with an argument or a counter-example. Back to the Geometry Online Index
Email any comments to lanius@math.rice.edu

##### Copyright 1997-2008 Cynthia Lanius

URL http://math.rice.edu/~lanius/Geom/irrat.html