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Subscribed: @Sherlychn @Javenieyong @Venicechua

[AfiqahSofry]

Hello! Well done with coming up with your codes! However, it would be great if you could visualise the random endpoints and random chords using ggplot. Also, it could be better to print the values of the probabilities on the console.

[alyaadis]

Hi! Nice work. However, I think it would be better to plot/visualise the chords and endpoints (circle) by using ggplot.
Also, maybe add more comments to make the code clearer and print the probabilities for each method as the output, so it would be easier to see instead of looking it from the global environment.

[azwaien]

Hello, the code seems fine.

However, the solution is provided in the environment section but there is no output. :(

Also, I tried to change the n from n = 100 to n = 100,000 (for checking) but the probability doesn't seem to converge. :(

Overall, Well done! and your code styling seems decent as well :D

[Alidinie]

The coding style is easy to understand. The probability for all methods can be seen in the environment but it would be nice if you guys printed the probability values and used ggplot to visualise the chords.

[wafi0]

Good effort in writing the code. The comments make it easier to understand.

It's unfortunate that the expected outcome (expected Pr(A) values [0.33, 0.5, 0.25]) couldn't be reached, but at least the code runs without any syntax errors and some parts do work correctly e.g. applying trigonometry, finding probability from existing samples

Suggestion:

Put variables inside round brackets to print their values in the console
E.g

# Estimated probability of chord being longer than triangle side-----------------
probEstA=mean(lengthA>lengthSide) # Method A
probEstB=mean(lengthB>lengthSide) # Method B
probEstC=mean(lengthC>lengthSide) # Method C

(probEstA)
(probEstB)
(probEstC)

EDIT:

Just want to quickly bring up the error that prevented the expected results, in case it's found to be useful. It's within the chord endpoint computations for methods A (which is actually method C in the instruction) and B.

Original code snippet:

# Calculate Chord endpoints - Method A
xA1 = (ax+pA)*(cos_angleA+qA)*(sin_angleA)
yA1 = (ay+pA)*(sin_angleA-qA)*(cos_angleA)
xA2 = (ax+pA)*(cos_angleA-qA)*(sin_angleA)
yA2 = (ay+pA)*(sin_angleA+qA)*(cos_angleA)

# Calculate Chord endpoints - Method B
xB1 = (ax+pB)*(cos_angleB+qB)*(sin_angleB)
yB1 = (ay+pB)*(sin_angleB-qB)*(cos_angleB)
xB2 = (ax+pB)*(cos_angleB-qB)*(sin_angleB)
yB2 = (ay+pB)*(sin_angleB+qB)*(cos_angleB)

# Original results
> (probEstA)
[1] 0.81553
> (probEstB)
[1] 0.65221
> (probEstC)
[1] 0.33436

Correct code snippet:

# Calculate Chord endpoints - Method A
xA1 = (ax+pA)*cos_angleA + qA*sin_angleA
yA1 = (ay+pA)*sin_angleA - qA*cos_angleA
xA2 = (ax+pA)*cos_angleA - qA*sin_angleA
yA2 = (ay+pA)*sin_angleA + qA*cos_angleA

# Calculate Chord endpoints - Method B
xB1 = (ax+pB)*cos_angleB + qB*sin_angleB
yB1 = (ay+pB)*sin_angleB - qB*cos_angleB
xB2 = (ax+pB)*cos_angleB - qB*sin_angleB
yB2 = (ay+pB)*sin_angleB + qB*cos_angleB

# More precise results
> (probEstA)
[1] 0.24882
> (probEstB)
[1] 0.5001
> (probEstC)
[1] 0.33056

Above is the expected combination of approximate Pr(A) values for random midpoints, random radial points, and random endpoints respectively.