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Nspired Proofs Conference: Modeling Functions in Math Discovery

Dive into advanced mathematics at the Nspired Proofs Conference in Kilgore, TX. Explore modeling functions, analyze data, and compare theoretical vs. actual results. Join Dr. Steve Armstrong from LeTourneau Univ. for an interactive session. Get ready for hands-on activities and engaging discussions!

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Nspired Proofs Conference: Modeling Functions in Math Discovery

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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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