Search Results for “ratio”
Golden Ratio
Euclid’s construction of the Golden Ratio is given step by step. Set t to values 1,2,3,4 to see the different steps. Or press Go and be patient. Euclid’s proof of this construction is here.
Simple Similar Triangles
Drag points A, B, and C to change the size and shape of the blue triangle, and its white counterpart that is similar (constrained by proportional SAS). Drag the Red point D to change the ratio in sizes. Observe the multitude of calculated output lengths and angles, and how they match the proportion value, proving similarity, regardless of the triangles' shapes/sizes.
Crank Slider
For a given input force at the slider C, this app calculates the torque generated at the crank AB. You can observe the ratio of output torque to input force is displayed, along with geometric quantities which can be used to compute this ratio.
5 bar toy variable radius
The physical pattern drawing toy has a fixed gear ratio of 6:1, giving hexagonal symmetry to the drawings. In software it is easy to make the gear ratio variable. Press the radius button to change the radius of the turntable
Bhaskara’s Proof
This app allows you to explore algebraic proof by the ancient Hindu mathematician Bhaskara, who used the properties of similarity to prove the theorem.
Optimal Performance of Box Solar Cooker
The solar concentration ratio of a solar cooker is the ratio of the amount of sunlight concentrated on the target to the size of the target. This model presents the best situation for a given lid angle, and lets you see how much light can be captured at that lid angle. The question is: what lid angle captures the most sunlight?
Parallelogram area
Points E, F, G, H are proportion p along line segments AB, BC, CD, DE respectively. How does the ratio of the shaded parallelogram to the area of ABCD depend on p?
Euclid Book 6 Proposition 19
Similar triangles are to one another in the duplicate ratio of the corresponding sides.
Pendulums
Change the ratio of the mass at B to the mass at C. Try and match the speed of the pendulum FG.
