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Masterclass Mentorship Team C

Masterclass Mentorship Team C. 1 dimension and 0 dimensions: A research on the relationship betweeen points and lines. A research and presentation by Cai Yi Zhan, Tan Wei Chuan, Darryll Chong, Lim Jan Jay and Ryan Wee. What we had to do. Our Research Question.

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Masterclass Mentorship Team C

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  1. Masterclass Mentorship Team C 1 dimension and 0 dimensions: A research on the relationship betweeen points and lines A research and presentation by Cai Yi Zhan, Tan Wei Chuan, Darryll Chong, Lim Jan Jay and Ryan Wee

  2. What we had to do

  3. Our Research Question What is the minimum number of point needed to form n straight lines? Conditions: • Line passes through exactly 2 points • Point of intersection not counted as a point, • Original point not said to be an intersection point • n >/= 1

  4. Illustrations Counted as a point 4 points are needed for 6 lines Intersection Point – not a point

  5. Proof • Let us start by showing the results if n= 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10.

  6. Proof • Pattern observed: • Periodical increase by 1 of the number of dots needed, • Period of 1 for 2 dots, 2 for 3 dots and 3 for 4 dots… … so on and so forth. • Prove that this will always happen

  7. Proof • Each value of no. of points will stay on for (no. of points-1) values of n: • Assume no. of points is k • When add another point (total now k+1), still k-1 more dots for new dot to join • (k+1)-(k-1)=2 • Therefore, k-2 more lines to be drawn. • Add the first line: therefore the no. of dots will always stay on for (no. of dots-1) values of n

  8. Proof • Will always be consecutive increase • Finding minimum number of dots • As proven, add 1 dot have (no. of dots – 2) more options • So, always increase of 1

  9. Proof - Formula • If the following is true, when b is the subtraction that will bring the total to or below zero: • [([(n-1)-2]-3)…- (b-1)] • Then the number of dots is: • ((b-1)+1)+1 • = b+1

  10. How we found the formula • Already know that no. of dots stays on for (no. of dots-1) values of n • Assume: • No. of dots 2 – 1st category • No. of dots 3 – 2nd category … … • The no. of dots is the category+1 • To find the category: • Utilize fact that no. of dots are consecutive • Start by subtracting 1, than 2

  11. How we found the formula • To find the category (continued): • Subtraction that brings total to or below 0 then category number, as: • 1 number in category 1 • 2 numbers in category 2 … … • In the formula that is b (category number). • So, (b-1)+1 is the category number • Add another 1 for no. of dots: • ((b-1)+1)+1 • = b+1

  12. Why we chose the thopic

  13. Difficulties

  14. Strengths

  15. Weaknesses

  16. Timeline Start Session 1 Delegated roles and created a wikispace Session 2 Posted a few questions based on a given situation and presented it Session 3 Discussed on proving a question's answer and learnt how to prove using mathematical induction and contradiction Session 4 Posted the problem that we were going to solve and prove and presented it. Listened to other presentations to get ideas in case of rejection. Session 5 Discussed about our answer and proof and presented 1st draft to Dr Soon Session 6 End Session 7 Session 8 (Now) Present problem,solution, proof......( basically everything)

  17. Learning Journey

  18. Reflections

  19. Acknowledgements • Dr. Soon, the expert mentor • Mr. Goh for helping us • Families of members who encouraged them • Members of team who did the project • Our Math Teachers who guided us

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