Broken/Mended Heart

The procedure for making the heart is as follows. The diagrams were made with Paint Shop Pro.

	Beginning with the white side facing up, fold paper in half. Fold sides to this halfway mark. This is commonly called a cupboard fold.
	Place the vertical side edge so it lines up with the horizontal top edge. Only crease where indicated.
	Repeat with other edges to form a square. Turn over.
	Place bottom edge so it lines up with the opposite bottom side of the square just folded. Only crease where indicated.
	Repeat with other edges to form diamond.
	Reinforce creases. The folds making up the square should be in the opposite direction as the folds making the diamond. Collapse into heart.
	Reverse-fold tips into the model to make the model more heart shaped.

The heart in both of its forms. To transform heart, pull apart lobes to reveal square (or diamond). Let the square (or diamond) fold in half as it should naturally.

This animation, made with Animation Shop, shows how to break and mend the heart.

• What are the measurements to make to define the shape and size of this model? This is a much more sophisticated question then 'how big is it'? A rectangle is defined by its length and its width. A square has single measurement. What are the measurements that completely specify a heart? This question becomes somewhat more complex since the final shaping folds are called 'cosmetic' and are 'to taste'. You can apply your analysis to the model before or after the cosmetic folds. Note: you want to make the measurements for both hearts. When you define these measurements, you can perform the task we have suggested before: compute the dimensions of the final model in terms of the dimensions of the original piece of paper.
• Having performed the previous step, now compare the two hearts. Are they similar (congruent) hearts? How are they alike and how are they different? What parts of one correspond to what parts of the other? What function is served by the shaping folds?
• What is making the action? That is, what folds are involved when the heart is transformed from one step to another. What parts of the paper are the hinge or pivot of the transformation?
• Try to compute the area of each heart. This could also be done before the shaping folds. Color the exposed parts as was done in the water bomb. See if you can predict how this will look when the model is unfolded.