Palindromic Pentagonals

http://www.worldofnumbers.com/penta.htm

Numbers that are not the sum of 3 pentagonal numbers http://oeis.org/A003679

Hexagonal Number #2

http://mathworld.wolfram.com/HexagonalNumber.html

http://www.worldofnumbers.com/hexa.htm

Heptagonal Number

http://mathworld.wolfram.com/HeptagonalNumber.html

http://www.worldofnumbers.com/hepta.htm

Octagonal Number

http://mathworld.wolfram.com/OctagonalNumber.html

http://www.worldofnumbers.com/octa.htm

Nonagonal Number #2

http://mathworld.wolfram.com/NonagonalNumber.html

http://www.worldofnumbers.com/nona.htm

Palindromic number records

A 53-digit Palindromic Square Number:

122063831551139898460740721 ^ 2 = 14899578972945056149893218681239894165054927987599841

http://blogs.msdn.com/b/fyuan/archive/2008/01/15/a-53-digit-palindromic-square-number.aspx

Other palindromic number records can be found at

http://www.worldofnumbers.com/palrecs.htm

http://www.worldofnumbers.com/square.htm

Invariance in Orthodiagonal Quadrilaterals

http://www.cut-the-knot.org/Curriculum/Geometry/DynamicsOfOrthodiagonalQuadrilaterals.shtml