Pythagorean Triangle with Sides in Arithmetic Sequence/Mistake
Jump to navigation
Jump to search
Source Work
1986: David Wells: Curious and Interesting Numbers:
- The Dictionary
- $5$
1997: David Wells: Curious and Interesting Numbers (2nd ed.):
- The Dictionary
- $5$
Mistake
- The $3-4-5$ triangle is the only Pythagorean triangle whose sides are in arithmetical sequence.
It needs to be pointed out that, as David Wells has defined Pythagorean triangle, $6-8-10$ is also a Pythagorean triangle, and $6, 8, 10$ is an arithmetical sequence.
The correct statement needs to include the condition that the sides form a primitive Pythagorean triple.
Sources
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $5$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $5$