REAL NUMBERS and the number line. Math 230 Presentation By Sigrid Robiso. Rational Numbers. The ancient Greeks created a reasonable method of measuring What is a rational number? Is every number a rational number?. Euclid. Pythagorean Theorem. Pythagoras
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Math 230 Presentation
By Sigrid Robiso
a² + b² = c²
a² + b² = c²
example if a= 1 and b= 1
1² + 1² = c²
c= √ 2
which is an irrational number because it is not equal to the ratio of two numbers
1. Build a square whose base is the interval from 0 to 1
2. Next draw the diagonal from 0 to the upper right corner of the square
3. Using a compass copy the length of that diagonal line onto the number line and make a mark
which makes us question is there a uniform method to label every point on the line- rationaland irrational?
√ 2 = 1.414213562…
The number left to the decimal point shows that our number will be somewhere between 1 and 2
Where? We cut the interval from 1 to 2 into 10 equal pieces
The next digit, 4, tells us in which small interval our number is located. We then take that small interval and cut it up into 10 very small equal pieces
The next digit, 1, tells us which very small interval our number resides
√ 2= 1.414213562….