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Discovery Nspired Proofs

Discovery Nspired Proofs. T 3 Regional Conference Kilgore, TX Dr. Steve Armstrong LeTourneau Univ. What Do You Think?. What if robot on a curved path approaches wall What would be modeling function for (time, dist) ordered pairs?. Diagram. Nspire screen. 16 in. r = 12 in. Manipulate.

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Discovery Nspired Proofs

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  1. Discovery Nspired Proofs T3 Regional Conference Kilgore, TX Dr. Steve ArmstrongLeTourneau Univ.

  2. What Do You Think? • What if robot on a curved path approaches wall • What would be modeling function for (time, dist) ordered pairs?

  3. Diagram • Nspire screen 16 in. r = 12 in

  4. Manipulate • Grab tangent point • Drag around circle • Note changing (angle, length)

  5. Acquire Data • Recordorderedpairs

  6. Prepare for Plot • Data captured automatically • Readyfor plotting • Guess curveshape first

  7. Scatter Plot

  8. Results • Note curve • More guessesas to modelingfunction?

  9. Analysis • Beginproof

  10. Analysis • Note right triangles • Central angle  repeats • Use trig ratios

  11. Modeling Function • Given • r = 12 • WN = 16 • Determine lengthof PW in termsof 

  12. Modeling Function • Given • r = 12 • WS = 16 • Determine lengthof PW in termsof 

  13. Results • Functiongraphed

  14. Experimental Results Ultrasonic sensor returns it's max value – "infinite" distance

  15. Matching Data to Analysis

  16. Experimental Results Good data for

  17. Experimental Results • Minimum interior sensorangle 75

  18. Resolving Theoretical vs. Actual

  19. Resolving Theoretical vs. Actual

  20. Resolving Theoretical vs. Actual • Nspire graph using degrees • Excel graph (actual data) using time (seconds) • But

  21. Final Results • Nspiredata points • Theoreticalfunction • NXT datapoints

  22. Challenge • Find a non trivial set of data • Given : what is the path of the vertex when you change the value of b? • Have the NXT robot follow a sine curve and measure time and distance • What happens to the area of an ellipse as you alter one of the coefficients? • What else ….. ?

  23. Challenge • Plot results with technology • Use same technology to analyze • Compare theoretical to actual data • And hope it matches 

  24. Any Questions?

  25. Discovery Nspired Proofs T3 Regional Conference Kilgore, TX Dr. Steve ArmstrongLeTourneau Univ.

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