The Euler and Grace-Danielsson inequalities for nested triangles and tetrahedra: a derivation and generalisation using quantum information theory

Author:

Milne Antony

Publisher

Springer Science and Business Media LLC

Subject

Geometry and Topology

Reference16 articles.

1. Bottema O., Djordjević R.Z., Janić R.R., Mitrinović D.S., Vasić P.M.: Geometric inequalities. Wolters-Noordhoff Publishing, Groningen (1969)

2. Balk A.M., Balk M.B.: The enigma of the triangular pyramid. J. Geom. 62, 13–25 (1998)

3. Mitrinović D.S., Pečarić J.E., Volenec V.: Recent advances in geometric inequalities. Springer, Berlin (1989)

4. Grace J.H.: Tetrahedra in relation to spheres and quadrics. Proc. Lond. Math. Soc. 17, 259–271 (1918)

5. Danielsson, G.: Proof of the inequality $${d^{2} \leq (R+r)(R-3r)}$$ d 2 ≤ ( R + r ) ( R - 3 r ) for the distance between the centres of the circumscribed and inscribed spheres of a tetrahedron, Den 11te Skandinaviske Matematikerkongress, Trondheim, 1949, pp. 101–105. Johan Grundt Tanums Forlag, Oslo (1952)

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1. On the Grace–Danielsson inequality for tetrahedra;Discrete Applied Mathematics;2019-03

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