1 / 19

# Masterclass Mentorship Team C - PowerPoint PPT Presentation

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.

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

Masterclass Mentorship Team C

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

## 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

### 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

### Illustrations

Counted as a point

4 points are needed for 6 lines

Intersection Point – not a point

### Proof

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

### 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

### 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

### 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

### 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

### 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

### 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

### 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)

### 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