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433 results

Page 1 of 22

  • Calculus by Amber Habib, pp 391, £49.99 (paper), ISBN 978-1-00915-969-2, Cambridge University Press (2022)

  • Nick Lord
  • Journal:
    The Mathematical Gazette / Volume 108 / Issue 573 / November 2024
    Published online by Cambridge University Press:
    12 November 2024, pp. 564-565
    Print publication:
    November 2024
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  • 108.35 Analogues of the 12 pentagons theorem for other families of polyhedra

  • Nick Lord
  • Journal:
    The Mathematical Gazette / Volume 108 / Issue 572 / July 2024
    Published online by Cambridge University Press:
    23 August 2024, pp. 351-352
    Print publication:
    July 2024
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  • Two quick direct proofs of the irrationality of tan15°

  • Nick Lord
  • Journal:
    The Mathematical Gazette / Volume 108 / Issue 572 / July 2024
    Published online by Cambridge University Press:
    23 August 2024, pp. 356-358
    Print publication:
    July 2024
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  • Infinite sums of reciprocal quadratics

  • Nick Lord
  • Journal:
    The Mathematical Gazette / Volume 108 / Issue 572 / July 2024
    Published online by Cambridge University Press:
    23 August 2024, pp. 358-362
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    July 2024
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  • A cautionary tale about the pole of polar coordinates

  • Nick Lord
  • Journal:
    The Mathematical Gazette / Volume 108 / Issue 571 / March 2024
    Published online by Cambridge University Press:
    15 February 2024, pp. 162-163
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    March 2024
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  • Another appearance of the golden ratio

  • Nick Lord
  • Journal:
    The Mathematical Gazette / Volume 108 / Issue 571 / March 2024
    Published online by Cambridge University Press:
    15 February 2024, pp. 163-165
    Print publication:
    March 2024
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  • Comic sections plus by Des MacHale, pp. 264, £15.67 (paper), ISBN 978-1-4717-6147-8 Logic Press (2022)

  • Nick Lord
  • Journal:
    The Mathematical Gazette / Volume 108 / Issue 571 / March 2024
    Published online by Cambridge University Press:
    15 February 2024, pp. 190-191
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    March 2024
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  • Infinitely many composites

  • Nick Lord, Des MacHale
  • Journal:
    The Mathematical Gazette / Volume 108 / Issue 571 / March 2024
    Published online by Cambridge University Press:
    15 February 2024, pp. 20-26
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    March 2024
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  • In number theory, we frequently ask if there are infinitely many prime numbers of a certain type. For example, if n is a natural number:

    1. (i) Are there infinitely many (Mersenne) primes of the form 2n − 1?

    2. (ii) Are there infinitely many primes of the form n2 + 1?

    These problems are often very difficult and many remain unsolved to this day, despite the efforts of many great mathematicians. However, we can sometimes comfort ourselves by asking if there are infinitely many composite numbers of a certain type. These questions are often (but not always) easier to answer. For example, echoing (i) above, we can ask if there are infinitely many composites of the form 2p − 1 with p a prime number but (to the best of our knowledge) this remains an unsolved problem. Of course, it must be the case that there are either infinitely many primes or infinitely many composites of the form 2p − 1 and it seems strange that we currently cannot decide on either of them.

  • 108.18 A one-line proof of the Finsler-Hadwiger inequality

  • Nick Lord
  • Journal:
    The Mathematical Gazette / Volume 108 / Issue 571 / March 2024
    Published online by Cambridge University Press:
    15 February 2024, pp. 158-160
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    March 2024
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  • The Devil’s Advocate and the binomial expansion

  • Nick Lord
  • Journal:
    The Mathematical Gazette / Volume 108 / Issue 571 / March 2024
    Published online by Cambridge University Press:
    15 February 2024, pp. 161-162
    Print publication:
    March 2024
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  • Euler’s prime-producing polynomial revisited

  • Robert Heffernan, Nick Lord, Des MacHale
  • Journal:
    The Mathematical Gazette / Volume 108 / Issue 571 / March 2024
    Published online by Cambridge University Press:
    15 February 2024, pp. 69-77
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    March 2024
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  • Euler’s polynomial f (n) = n2 + n + 41 is famous for producing 40 different prime numbers when the consecutive values 0, 1, …, 39 are substituted: see Table 1. Some authors, including Euler, prefer the polynomial f (n − 1) = n2 − n + 41 with prime values for n = 1, …, 40. Since f (−n) = f (n − 1), f (n) actually takes prime values (with each value repeated once) for n = −40, −39, …, 39; equivalently the polynomial f (n − 40) = n2 − 79n + 1601 takes (repeated) prime values for n = 0, 1, …, 79.

Page 1 of 22