Some Proofs of the Existence of Irrational Numbers
... Clearly, we can repeat this process of constructing a new square indefinitely, with each new square strictly smaller than the last. Note also that, inductively, the sides and diagonal of each new square are measured by our original e. This is a contradiction by infinite descent: for example, suppose ...
... Clearly, we can repeat this process of constructing a new square indefinitely, with each new square strictly smaller than the last. Note also that, inductively, the sides and diagonal of each new square are measured by our original e. This is a contradiction by infinite descent: for example, suppose ...
a Microsoft Word document containing a review sheet for
... Tips for Proving Trigonometric Identities: Sometimes it helps to write everything as sines and cosines. Look for pieces that can be simplified using the Pythagorean Identities. Sometimes it helps to multiply things out. Sometimes it helps to factor things. Sometimes you’ll have to find com ...
... Tips for Proving Trigonometric Identities: Sometimes it helps to write everything as sines and cosines. Look for pieces that can be simplified using the Pythagorean Identities. Sometimes it helps to multiply things out. Sometimes it helps to factor things. Sometimes you’ll have to find com ...
A Brief History of Pi
... root of any algebraic equation with rational coefficients. This discovery proved that you can't "square a circle", which was a problem that occupied many mathematicians up to that time. (More information on squaring the circle.) How many digits are there? Does it ever end? Because Pi is known to be ...
... root of any algebraic equation with rational coefficients. This discovery proved that you can't "square a circle", which was a problem that occupied many mathematicians up to that time. (More information on squaring the circle.) How many digits are there? Does it ever end? Because Pi is known to be ...
