Search

Search Results

• Proof without words: beyond the parallelogram law

  153-156

  C. Alsina

  A. Monreal

  Views:

  21

  We present a visual proof of the parallelogram law and using it we can describe a visual proof of a classical theorem on convex quadrilaterals relating sides and diagonals.

• Proof without words: Knopp series for (pi)

  451-452

  Ángel Plaza

  Views:

  30

  There are many expressions for number π as infinite series or infinite product (see for example [1, 2, 3]). In [1] the following series for number π is attributed to K. Knopp:...

• Proof without words

  207

  Ángel Plaza

  Views:

  6

  | cos α + sin α | ≤ √2 with equality…

• Proof without words: (a + b)^3 = a^3 +3a^2b +3ab^2 + b^3

  157

  C. Alsina

  A. Monreal

  Views:

  7

  (a+b)^2…

• Proof without words

  311-312

  Zoltán Kátai

  Views:

  5

  Let us prove: If we add 1 to the product of four consecutive natural numbers, we get a square number:…

• Proof without words: four circles

  307-309

  Ángel Plaza

  Views:

  10

  Theorem. Let O, P and Q be three points on a line, with P lying between O and Q. Semicircles are drawn on the same side of the line with diameters OP, PQ and OQ. An arbelos is the figure bounded by these three semicircles. Draw the perpendicular…

• Proof without words: limit of a recursive sequence

  121-122

  Pilar Abreu

  Esther Guerra

  Ángel Plaza

  Views:

  2

  x_0 > 0 …

• Proof without words: partial sum and sum of a geometric series

  423

  Ángel Plaza

  Views:

  4

  Let r be a positive real number such that 0 < r < 1, then:…