|The Farmer and the Mathematician 2|
| The farmer is back, and he has a new mathematical friend helping him to make more sophisticated analyses of how best to use his central pivot irrigation equipment.|
Packing circular segments into rectangles, triangles and trapezoids uncovers interesting geometry problems with theoretical as well as practical implications.
That and some really bad puns.
Preview the book here.
For example, a css which positions every element in the center of the window, rather than left justified would look like this:
An app using the above style sheet can be viewed here.
Problem of the Month
ABCDEFG is a regular heptagon.
I is the intersection of BD and CE, J is the intersection of CF and BE, K is the intersection of CG and BF, L is the intersection of AC and BG.
Show that B,C,I,J,K,L are vertices of a regular heptagon.
An interactive illustration is here
Can you generalize this result?
January Problem Solution:
CAD is an arc of a parabola with vertex A and focus B.
FGHI is the control polygon of a cubic spline.
Can you locate points FGHI so that the spline is exactly the parabolic arc?
If so, where?
An interactive app which lets you play with this problem is here.
Clearly F and I should lie on C and D, and FG and IH should be tangents to the parabola. Playing with the interactive app suggests that positioning H and G 2/3 of the way to their intersection yields a good approximation to the parabola.
Is this exact? A Geometry Expressions model confirms that it is:
- The Tortoise and Achilles
- Calculus Explorations
- The Farmer and the Mathematician
- Developing Geometry Proofs
- 101 Symbolic Geometry Examples
- 101 Conic Sections Examples
- Using Symbolic Geometry to Teach Secondary School Mathematics
- Connecting Algebra and Geometry through Technology
- Function Transformations
- Exploring with Geometry Expressions
- The Farmer and the Mathematician II
Sample chapters of other iPad eBooks are available here
Interactive math Apps which can be viewed on your iPad are available from Euclid's Muse
See our YouTube channel
for videos exploring features in Geometry Expressions.
Watch more videos about creating Apps with Geometry Expressions.
Learn how to Export an Animation with Geometry Expressions.