specail

mmwu, Mar 18, 2015


  • 1. The Sum of the Cubes of the First N Natural Numbers
  • 2. Prostopadłościan
  • 3. Symetralna / Perpendicular bisector
  • 4. Kąt dwuścienny
  • 5. Dwusieczna kąta / Bisector
  • 6. Prosta prostopadła / Perpendicular
  • 7. Okrąg opisany na trójkącie / Circumcircle of triangle

1.

The Sum of the Cubes of the First N Natural Numbers

This applet shows a dynamic geometric proof of the formula for the sum of the cubes of the first [math]n[/math] natural numbers.[br][list][br][*]Drag the slider “NumberCubes” to create up to seven cubes.[br][/list][br]Think of each cube as a collection of [math]n[/math] square layers of [math] n \times n[/math] unit cubes. To find a formula for the sum of the cubes of the first natural numbers we will rearrange the square layers.[br][list][br][*]Drag the slider “Rearrange” or press the “animate” button.[br][br][/list]
– Irina Boyadzhiev

2.

–

3.

–

4.

–

5.

–

6.

–

7.

–

Information