What are Illustrations of formulas?
Formulas are statements of algebra, which apply to numbers of a definition set.
They can be proved except the axioms. You can deduce new formulas by well-known formulas by logical reasoning. This procedure is called a proof.
The proof ideas and also the proof ways can be described by pictures. In addition the formulas themselves become more alive.
You can find illustrations of well known formulas on this page.
Simple Formulas top
Product of a difference and a number
Product of two sums
Product of two differences
Product of a sum and a difference
Looking for a parallelogram with the same area
Binomial Formulas top
Second binomial formula
Third binomial formula
Difference of the squares of a sum and a difference
Pythagoras's Theorem top
The Pythagorean theorem (Pythagoras or one of his students, Pythagoras of Samos, 580-500 BC)
Classical proof with triangles
The Pythagorean theorem (Euklid, ~300 BC)
Proof with four-sided figures
Euklid's theorem (Euklid, ~300 BC)
The Pythagorean theorem (Liu Hui, ~300, China)
The Pythagorean theorem ("The bride's chair", ~900, India)
The Pythagorean theorem (Atscharja Bhaskara, Indien, ~1150)
The Pythagorean theorem (Leonardo da Vinci, 1452-1519)
The Pythagorean theorem (Arthur Schopenhauer's case was a=b, 1788-1860)
The Pythagorean theorem (James Garfield 1876, later on the 20th US President)
The Pythagorean theorem (Hermann Baravalle 1945)
The Pythagorean theorem
(a+b)²=c²+4*(1/2ab) oder a²+b²=c²
You can see both cubes and the six rectangular parallelepipeds in 3D-view:
The formula is (a-b)³=a³-3a²b+3ab²-b³. You convert it to (a-b)³=a³-3ab(a-b)-b³ for an illustration.
This page is also available in German.
© 2002 Jürgen Köller