October 03, 2012
2-1 Patterns and Inductive Reasoning
Inductive Reasoning: making a conjecture/conclusion based on patterns or
previous examples
statement you believe to be true
Steps: 1. Look for a pattern
2. Make a conjecture (unproven statement based on observations)
3. Verify the conjecture is true for all cases
Worksheet 2-1: Do # 1-4
October 03, 2012
October 03, 2012
Find the next item in the pattern.
1. January, March, May, ...
2.
7, 14, 21, 28, ...
3.
4. 1, 2, 4, ...
October 03, 2012
Complete the each conjecture.
1. The sum of two positive numbers is ___________.
2. The number of lines formed by 4 points, no three of which
are collinear, is ___________.
Worksheet 2-1: Do #5-6
October 03, 2012
Goldbach's Conjecture:
Every even number greater than 2 can be written as the sum of 2
primes. (i.e. 44 = 13 + 31)
Think of some even numbers greater than 2 and how they can be
written as the sum of 2 primes.
October 03, 2012
October 03, 2012
Is it possible to show that Goldbach's Conjecture is true for all cases?
Why?/Why not?
To prove a conjecture is FALSE, you need a single
COUNTEREXAMPLE (example showing conjecture
is false)
Ex. Conjecture: The difference of 2 positive numbers is always positve.
Is the conjecture true or false? If false, give a counterexample.
October 03, 2012
Show that the conjecture is false by providing a counterexample.
1. Two complementary angles are not congruent.
Worksheet 2-1: Do #7-9
October 03, 2012
Ex. Make a Conjecture.
The sum of the first n odd positive integers is ?
Worksheet 2-1: Do #10-11