Jump to content

O'Halloran numbers: Difference between revisions

simplify preface
(it is not a conjecture)
(simplify preface)
Line 1:
{{draft task}}
 
For this task, for our purposes, a regular integer cuboid is a regular 3 -dimensional rectangular object, with six faces, where all angles are right angles, where opposite faces of the cuboid are equal, and where each dimension is a positive integer unit length. It will subsequently be referred to simply as a cuboid; but be aware that it references the above definition.
 
The surface area of a cuboid so-defined is two times the length times the width, plus two times the length times the height, plus two times the width times the height. A cuboid will always have an even integer surface area. The minimum surface area a cuboid may have is 6; one where the '''l''', '''w''', and '''h''' measurements are all 1.:
 
2 × ( l × w + w × h + h × l )
2 × ( 1 × 1 + 1 × 1 + 1 × 1 ) = 6
 
DifferentNotice cuboidthat configurationsthe (may) yield differenttotal surface areas,area butof thea surface areacuboid is always an integer and is always even.
 
AFor example, a cuboid with l = 2, w = 1 h = 1 has a surface area of 10:
 
2 × ( 2 × 1 + 1 × 1 + 1 × 2 ) = 10
 
ThereNotice there is no configuration which will yield a surface area of 8.
 
In fact, there are 16 even integer values greater than 6 and less than 1000 which can not be the surface area of any integer cuboid.
2,497

edits

Cookies help us deliver our services. By using our services, you agree to our use of cookies.