mscroggs.co.uk
mscroggs.co.uk

subscribe

Sunday Afternoon Maths XXXVIII

 Posted on 2015-02-01 

Products and sums of squares

Show that the product of any two numbers, each of which is the sum of two square integers, is itself the sum of two square integers.

Show answer & extension

Equal side and angle

In the diagram shown, the lengths \(AD = CD\) and the angles \(ABD=CBD\).
Prove that the lengths \(AB=BC\).

Show answer

Arctan

Prove that \(\arctan(1)+\arctan(2)+\arctan(3)=\pi\).

Show answer & extension

If you enjoyed these puzzles, check out Advent calendar 2023,
puzzles about perimeter, or a random puzzle.

Archive

Show me a random puzzle
 Most recent collections 

Advent calendar 2023

Advent calendar 2022

Advent calendar 2021

Advent calendar 2020


List of all puzzles

Tags

numbers symmetry regular shapes percentages algebra consecutive integers triangles 2d shapes complex numbers surds speed chocolate calculus graphs multiples crossnumbers sport partitions ellipses means odd numbers lines taxicab geometry crossnumber remainders digits proportion cards games cryptic clues angles logic people maths square numbers probability the only crossnumber averages differentiation sequences bases trigonometry functions integration coins palindromes volume fractions unit fractions chalkdust crossnumber factors cube numbers arrows crosswords even numbers quadratics christmas quadrilaterals decahedra spheres irreducible numbers tangents squares wordplay range pentagons geometric means grids shape square roots folding tube maps rugby matrices sets prime numbers cubics geometric mean 3d shapes hexagons dice ave scales albgebra colouring routes sum to infinity triangle numbers planes floors probabilty shapes gerrymandering polynomials binary integers number elections perimeter multiplication cryptic crossnumbers clocks menace combinatorics division dodecagons polygons parabolas expansions axes dominos time geometry factorials indices perfect numbers balancing star numbers circles dates products digital products digital clocks doubling addition advent mean consecutive numbers area coordinates tournaments median chess rectangles tiling pascal's triangle determinants money books sums

Archive

Show me a random puzzle
▼ show ▼
© Matthew Scroggs 2012–2024