Visually stunning math concepts which are easy to explain
When I look up "area of a rhombus" on Google images, I find plenty of disappointing images like this one: which show the formula, but fail to show why the formula works. That's why I really appreciate this image instead: which, with a little bit of careful thought, illustrates why the product of the diagonals equals twice the area of the rhombus. EDIT: Some have mentioned in comments that that second diagram is more complicated than it needs to be. Something like this would work as well: My main objective is to offer students something that encourages them to think about why a formula works, not just what numbers to plug into an equation to get an answer. As a side note, the following story is not exactly "visually stunning," but it put an indelible imprint on my mind, and affected the way I teach today. No wonder that, when I ask my college students if they can tell me the formula for the volume of a pyramid, fewer than 5% can. She continued: "Three," he said.
Related: MATH / GEOMETRY
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