No CrossRef data available.
Article contents
Ratios in Heronian triangles
Published online by Cambridge University Press: 18 June 2020
Extract
Heronian triangles are triangles with integer sides and area. In [1], a classical result about squares in arithmetic progression was obtained by proving that it is not possible for the altitude of a Heronian triangle to divide the base in the ratio of 1 : 2. In this article we shall investigate general ratios of the form 1 : n, where n is a positive integer. These base ratios do not appear to have received previous attention despite the wealth of results about other aspects of Heronian triangles [2].
Information
- Type
- Articles
- Information
- Copyright
- © Mathematical Association 2020
References
Dolan, S., Heronian triangles and squares in arithmetic progression, Math. Gaz. 103 (November 2019) pp. 490–493.CrossRefGoogle Scholar
Triangles, Heronian, Wikipedia, accessed January 2020 at https://en.wikipedia.org/wiki/Heronian_triangleGoogle Scholar
Pell’s equation, Wikipedia, accessed January 2020 at https://en.wikipedia.org/wiki/Pell’s_equationGoogle Scholar
Mazur, B., Rational isogenies of prime degree, Invent. Math. 44(2) (1978) pp. 129–162.CrossRefGoogle Scholar
Torsion conjecture, Wikipedia, accessed January 2020 at https://en.wikipedia.org/wiki/Torsion_conjectureGoogle Scholar
Bhargava, M. and Skinner, C., A positive proportion of elliptic curves over Q have rank 1, J. Ramanujan Math. Soc. 29(2) (2014) pp. 221–242.Google Scholar