. The segmentsare shownbelow.
B. For five points,no threepointsbeingcollinear, how manyline segmentswith thosepointsas endpoints
are there?
. Whenwe add a th point,thereis a new segmentfrom that pointto eachof the otherfour points.
We can drawthe four new dashedsegmentsshownbelow. Togetherwith the six segmentsfor the four
pointsin part A, this makes segments.
NumberPatterns
You are alreadyfamiliarwith manynumberpatterns.Hereare a few examples.
Example 4 – PositiveEvenNumbers
The positiveevennumbersform the patternWhatis the positiveevennumber?. Eachpositiveevennumberis morethan the precedingone. You couldstart with , then add ,
times,to get the number. But thereis an easierway, usingmoreadvancedmathematicalthinking.
Noticethat the evennumberis , the evennumberis , and so on. So the even
numberis
Example 5 – Odd Numbers