I created this polygonal Christmas tree with a polygonal star on Desmos, and it looks like it is living and breathing to me!
Later I saw this Christmas tree post and decided to share it here:
For anyone looking for a Christmas-themed Maths lesson which practises plotting quadratics and other non-linear graphs, check out these at https://t.co/Aamu6gBYQU
🎄🎅#mathsresources #mathschat #christmaths pic.twitter.com/r5HvOxra6l— Amanda Austin (@draustinmaths) December 13, 2023
Today’s Puzzle:
Can you find the factors that belong on this Christmas factor tree for 1768?
Factors of 1768:
- 1768 is a composite number.
- Prime factorization: 1768 = 2 × 2 × 2 × 13 × 17, which can be written 1768 = 2³ × 13 × 17.
- 1768 has at least one exponent greater than 1 in its prime factorization so √1768 can be simplified. Taking the factor pair from the factor pair table below with the largest square number factor, we get √1768 = (√4)(√442) = 2√442.
- The exponents in the prime factorization are 3,1 and 1. Adding one to each exponent and multiplying we get (3 + 1)(1 + 1) (1 + 1) = 4 × 2 × 2 = 16. Therefore 1768 has exactly 16 factors.
- The factors of 1768 are outlined with their factor pair partners in the graphic below.
More About the Number 1768:
1768 is the sum of two squares in two different ways:
38² + 18² = 1768, and
42² + 2² = 1768.
1768 is the hypotenuse of FOUR Pythagorean triples:
168-1760-1768, calculated from 2(42)(2), 42² – 2², 42² + 2²,
680-1632-1768, which is 136 times (5-12-13),
832-1560-1768, which is 104 times (8-15-17),
1120-1368-1768, calculated from 38² – 18², 2(38)(18), 38² + 18².
The first triple is also 8 times (21-220-221), and
the last triple is also 8 times (140-171-221).
1768 looks interesting in some bases you probably would never care about:
It’s 404 in base 21 because 4(21²) + 0(21) + 1(1) = 1768.
It’s 1Q1 in base 31,
YY in base 51, and
QQ in base 67.
Can you solve for Q and Y?