Discovery Nspired Proofs T 3 Regional Conference Kilgore, TX Dr. Steve Armstrong LeTourneau Univ.
-
Upload
natalie-chandler -
Category
Documents
-
view
212 -
download
0
Transcript of Discovery Nspired Proofs T 3 Regional Conference Kilgore, TX Dr. Steve Armstrong LeTourneau Univ.
Discovery Nspired Proofs
T3 Regional ConferenceKilgore, TX
Dr. Steve ArmstrongLeTourneau 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
• Grab tangent point• Drag around circle• Note changing (angle, length)
Acquire Data
• Recordorderedpairs
Prepare for Plot
• Data captured automatically
• Readyfor plotting
• Guess curveshape first
Scatter Plot
Results
• Note curve• More guesses
as to modelingfunction?
Analysis
• Beginproof
Analysis
• Note right triangles
• Central angle repeats
• Use trig ratios
Modeling Function
• Given• r = 12• WN = 16
• Determine lengthof PW in termsof
16
Modeling Function
• Given• r = 12• WS = 16
• Determine lengthof PW in termsof
12
16
Results
• Functiongraphed
16( ) 12 tan
cosf x x
x
Experimental Results12
16
r
d
Ultrasonic sensor returns it's max value – "infinite" distance
Ultrasonic sensor returns it's max value – "infinite" distance
Matching Data to Analysis
Experimental Results
Good data for 25 25
Experimental Results
• Minimum interior sensorangle 75 25
75
Resolving Theoretical vs. Actual
Resolving Theoretical vs. Actual
2
1
0.3312k
i i
i i
X O
O
Resolving Theoretical vs. Actual
• Nspire graph using degrees• Excel graph (actual data) using time (seconds)
• But ( )f t
Final Results
• Nspiredata points
• Theoreticalfunction
• NXT datapoints
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 ….. ?
2y a x b x c
Challenge
• Plot results with technology• Use same technology to analyze • Compare theoretical to actual data
• And hope it matches
Any Questions?
Discovery Nspired Proofs
T3 Regional ConferenceKilgore, TX
Dr. Steve ArmstrongLeTourneau Univ.