Search Results for “Geometry”
Euclids Elements – Book 3 – Proposition 08This proposition proves that line AD is longest, ED is shorter, FD is shorter than ED, and CD is even shorter.and that for any line there is only one other line with a point on the circle and a point at D that is equal. (Unless you drag it to somewhere it's not supposed to be) I like it because it’s colorful.
Circles, Tangents, and Heptagon DiagonalsTwo circles are centered at intersection points of diagonals of a regular hepatgon. It turns out that circles centered at intersection points in regular polygons (particularly interestingly with polygons of odd numbers of sides) can be tangent to many other diagonals of that polygon. Try resizing the circles by dragging the green points. How many diagonals can each circle be tangent to? Ready for more? Check out the nonagon version!
Euclids Elements – Book 1 – Proposition 47The famous Pythagorean Theorem. Can you see how it works?
Point TrilaterationUse any three points and their distances from a fourth point to locate the fourth point.
Euclids Elements - Book 1 - Proposition 45Creating a parallelogram equal to a given quadrilateral with a given angle.
Euclids Elements - Book 3 - Proposition 14Creating a tangent on a circle given point A that is outside the circle.
Euclids Elements - Book 1 - Proposition 01The very first proposition, in which Euclid creates a equilateral triangle from a straight line by using two circles.
Euclids Elements - Book 2 - Proposition 14One of my favorite apps because it looks deceptively simple, but takes some really creative thinking. This app creates a square (in red) that has the same area as a given quadrilateral.
Euclids Elements – Book 1 – Proposition 42To construct, in a given rectilineal angle, a parallelogram equal to a given triangle. In other words, given angle D and triangle ABC (in blue), construct a parallelogram (in yellow) that has an equal area to triangle ABC.
Euclids Elements – Book 4 – Proposition 11Can you create a regular pentagon without a protractor? Because it’s pretty impressive how Euclid did it with only a compass and a ruler. Note that the yellow triangle is similar to the one inside the pentagon.
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