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Showing posts from July, 2010

### Improve math skills of your kids - Learn step-by-step arithmetic from Math games

Math: Unknown - Step-by-step math calculation game for iOS.

Math: Unknown is much more than a math game. It is a step-by-step math calculation game which will teach users how to calculate in the correct order rather than just asking only the final calculated results.

The app consists of four basic arithmetic operations which are addition, subtraction, multiplication and division. In order to get started, users who are new to arithmetic can learn from animated calculation guides showing step-by-step procedures of solving each type of operation. It is also helpful for experienced users as a quick reference.

Generally, addition and subtraction may be difficult for users who just start learning math especially when questions require carrying or borrowing (also called regrouping). The app helps users to visualize the process of carrying and borrowing in the way it will be done on paper. Once users understand how these operations work, they are ready to learn multiplication and division.

For most students, division is considered as the most difficult arithmetic operation to solve. It is a common area of struggle since it requires prior knowledge of both multiplication and subtraction. To help users understand division, the app uses long division to teach all calculation procedures. Relevant multiplication table will be shown beside the question. Users will have to pick a number from the table which go into the dividend. Multiplication of selected number and divisor is automatically calculated, but the users have to do subtraction and drop down the next digit themselves. Learning whole calculation processes will make them master it in no time.

Math: Unknown is a helpful app for students who seriously want to improve arithmetic calculation skills.

### Polynomial Cam Function (Introduction) - Part 1

Fundamental Law of Cam Design

(1) The cam function must be continuous through the first and second derivatives of displacement across the entire interval (360 degrees)*

(2) The jerk function must be finite across the entire interval (360 degrees)*
* Source: Fundamentals of machine design 1st edition, Robert L. Norton, McGrawHill, page 388

Normally the motion from cam cannot be defined by only a single mathematical expression, it consists of different equation on each different segment e.g. sector A-B uses cycloidal motion, sector B-C has dwell function (R=constant), sector C-D uses cycloidal motion again to come back to its starting point, and sector D-A has dwell function. We don't combine these 4 segments into only one equation, but we separate the functions to define the movement of cam follower behavior over each segment and make sure that there is no discontinuity in the displacement, velocity and acceleration functions.

Any discontinuity in the acceleration function will lead…