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.