Euclid's Muse
your source for INTERACTIVE math apps
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Trapezoidal Sum Rule
This is an example of the Trapezoidal Sum Rule. Here we have the rough average rates of the water exiting the Columbia River at Bonneville Dam on the Oregon and Washington border between 1938 and 1998, where at x=0 is 1938 and every 5 years is marked by 10000x. So at x=120000, the year is 1998. The formula to find the integral of the data, or the sum of the amount of water that flowed out of Bonneville Dam in the 60 year interval, or even simply the sum of the areas of the trapezoids, is the equation: T = ((b – a)/(2n) ) [ f(x0 ) + 2 f(x1 ) + 2 f(x2 ) + ... + 2 f(xn-1 ) + f(xn ) ] When we use this equation,we find the sum of all the water that flowed from Bonneville Dam from 1938 to 1998 is 1,510,000,000 cubic meters of water. The values for the rate of water flow in the years 1963 and 1998 can be changed to show what would happen to the sum of the water if the flow rate was different for those years.
Soda Cantastrophy
Download app to see the effects of changing radius and rate of change on the area.
Double Transforming Pentagons
Two pentagons are nested within a third, regular pentagon (ABCDE). They are each defined by a point on each side of ABCDE; these points are proportional along their sides at functions of t. Determine the function of t that represents the proportionality of each point. Notice that both pentagons are congruent to ABCDE when t = 0 and t = 1.
If a Tree Grows in a Forest
This app explores related rates with a real-life example.
Tangent Lines
Use derivatives to demonstrate the concept of tangent lines with circles.
The Idea Behind Integrals
A real-life example is used to help illustrate the reasoning behind integrals.
Apparent Plane Speeds
This app demonstrates why planes appear to be traveling at different speeds when flying at different altitudes.
The Relationship Between Position and Velocity
Check out how velocity changes based on the position of an object at time t.
Lecture11-DerivativeOfALine
This applications demonstrates the relationship between a line centered at the origin and its derivative. From Lecture 11 of "Learning Calculus with Geometry Expressions" a multi-touch interactive book for tablet computers. http://goo.gl/wUSKK
Pythagorean Theorem Calculator
A simple Pythagorean Theorem calculator that accepts inputs for either two sides or one side and the hypotenuse, then calculates the remaining side using the Pythagorean Theorem. Both exact and approximate solutions are provided, as well as the complete Pythagorean Theorem version.Featured Collections
- Clocks
- Proportional Puzzlers
- Circles, Tangents, and N-gon Diagonals
- Trammels
- Rotating Ellipses
- Function Composition
- Fagnano's Problem
News
Geometry Expressions 3.1 Released
We’ve released Geometry Expressions 3.1 (if you have version 3.0, install the update by going to the Help->Check for Updates menu). This release features many new features aimed at improving apps for Euclid’s Muse. New features include: Several new features for generated JavaScript apps, Lua apps, and Dashboard Widgets: New input controls: Advance Button lets you [...]
Introducing Collections
We’ve recently launched an exciting new feature: collections. Collections allow you to group any public apps, including those that you didn’t upload, into one place. With collections, you can either view a table of contents which includes links to each app, or you can enter the collection and see each app page normally, but with [...]
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