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The Mathematical Gazette Nov 1999

Volume 83 Number 498

Editor Steve Abbott


Contents


Articles
   
Something interesting! (The 1999 Presidential Address) J. Chris Robson 386
What goes round comes round Victor Bryant 394
What shape is an ellipse? Ann E. Hirst 400
Families of ovals and their orthogonal trajectories D.F. Lawden 410
Simple mappings in mechanics Drago Bajc 421
Solitary Solarians and densely packed spheres Paul Stephenson 426
An isoperimetrical problem in n dimensions Werner Schindler 433
Divisors of n! Keith Hirst 440
Playing with Pythagoras and geometric arithmetic 446

Student Workshop
   
Decimal déj? vu John R. Silvester 453

Notes 83.46 to 83.69
   
Equifacial tetrahedra and a famous location problem Y.S. Kupitz and H. Martini 464
The Secret Santa problem Kelly M. McGuire, George Mackiw and Christopher H. Morrell 467
Some examples of the use of areal coordinates in triangle geometry J.A. Scott 472
Symmetric cubic functions and inequalities K. Robin McLean 477
Recent formulae for p: arctan revisited! Nick Lord 479
On a theorem of Brianchon and Poncelet Kenzi Odani and Shihomi Takase 483
A faster convergence to Euler's constant Tanase Negoi 487
A circuitous way to differentiate sin q Steve Abbott 489
Almost pavings of patios Reg Allenby 490
More on the formula for loops in a box Rodney Berrieman 492
An analytical proof of the generalised Steiner-Lehmus theorem Mowaffaq Hajja 493
Another problem for Carl Friedrich: on the sums Sni=1éi/pù and Sni=1ëi/pû Hans J.H. Tuenter 495
Hyperbolic Mensuration Graham Hoare 497
A brief note to prove Roth's removal rule A.J.B. Ward 499
The mathematics of equal temperament John B. Reade 500
Irrational roots Colin Richard Hughes 502
A trigonometric proof of a trigonometric inequality M. Drukker 503
A definite integral via a difference equation Frank Chorlton 504
No converse to Lagrange's theorem Bob Burn 505
Numbers and their digits - II S. Parameswaran 506
A 'radical' definition for sample variance Gerald Newth 507
Why Simpson's rule gives exact answers for cubics Raymond N. Greenwell 508
A simple proof of the Lagrange identity on vector products Manuel Álvarez and Joaqu?n M. Gutiérrez 509
The velocity vector as Pinocchio's nose Stephen Warr 509

Correspondence
 
511

Problem corner

G. T. Q. Hoare

514

Students problems

Tim Cross

519

40th International Mathematical Olympiad

Imre Leader

522

Other Journals

Anne C. Baker

529

Book Reviews
 
533

Acknowledgements
 
574

For further information about The Mathematical Gazette please contact the Editor.