The+Paper+Fold

__The Paper Folds__
Amanda, Christina, Claudia, Mai

Purpose** is to find a model where the crease, 2z can be calculated by measuring the length and the width of a paper. Data needed to be collected: a= the length of the paper (optional) b= the width of the paper (needs to be measured) x = the part of paper that is not covered when folded. 2z = the crease made between point C and B
 * 1. The Crease Length
 * Materials** needed are a ruler and a sheet of paper.



When put together (provided that you have the values "a", "b" and "x" - or length, width and uncovered length), the equation would be:

can be used using the data collected.
 * Conclusion:** In order to find the length of the crease of a paper, the length and the width of the paper needs to be measured. After that, the model:

Purpose** is to determine the triangle with sides y and x that have the largest area.
 * 2. The Largest Triangle
 * Materials** are once again a ruler and a sheet of paper.

Data Collected:

Size of paper: 21.6 by 27.9
 * //Trial// || //x// || //y// ||
 * 1 || 14.3 || 6.3 ||
 * 2 || 8.7 || 9.0 ||
 * 3 || 10.3 || 4.1 ||
 * 4 || 17 || 4.2 ||

Calculations:

Area of Triangles -

Graphed in calc : Cubic Regression found in Calculator:
 * x (cm) || Area (cm^2) ||
 * 14.3 || 45.0 ||
 * 8.7 || 39.2 ||
 * 10.3 || 21.1 ||
 * 17 || 35.7 ||

Find the maximum area of the triangle by locating its maximum point on the concave curve of the cubic equation. Point: (15.46, 52.68)


 * Conclusion:** The maximum possible area of a triangle by folding one opposite corner to a side is 52.68cm^2, when x is at 15.46 cm.