Today’s Puzzle:

Merry Christmas, everybody! Can you make a Christmas design in Desmos?

Here’s how I solved this Desmos Christmas puzzle: A few weeks ago, I saw this post on Bluesky and was inspired by the climbing sine curves on the featured Desmos Christmas tree:

#mathstoday I began thinking about a Desmos activity for my year 11 in which they could make a Christmas tree. Then I got carried away, thought about climbing sine curves (tinsel) and translating polar graphs. I’m not sure it’s suitable for year 11 anymore… Oops

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— over-drawn.bsky.social (@over-drawn.bsky.social) November 28, 2024 at 12:34 PM

What is a climbing sine curve, and could I use one to decorate the plain Desmos Christmas tree I made last year? I had to google “climbing sine” to proceed, but I learned that it is a function such as y = x + sin(x). That’s a familiar function; I just didn’t know it had a cutesy name.

I multiplied that function by a constant. Can you figure out what that constant was?

Later, I embellished the tree even more with lights and falling snow. I hope you enjoy it!

Here are some other delightful Christmas Desmos designs I saw on Bluesky. this first one rotates in 3-D.

Happy Holidays! 🎄
http://www.desmos.com/3d/p5t7m4kh4s
#iTeachMath

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— Raj Raizada (@rajraizada.bsky.social) December 10, 2024 at 10:46 AM

Enjoyed re-creating this visual in the @desmos.com Geometry tool: http://www.desmos.com/geometry/lx7… #mathsky

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— Tim Guindon (@tguindon.bsky.social) December 11, 2024 at 1:08 PM

More snowflake fun in @desmos.com
I don’t think it can show text mirror-flipped yet (?), so for this, you type your word, screenshot it, then load it as an image.
I’m hoping to have students load in pics of their names, then snowflake-ify them.
http://www.desmos.com/geometry/afo…
#iTeachMath #MathSky

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— Raj Raizada (@rajraizada.bsky.social) December 17, 2024 at 11:17 AM

This next one isn’t a Desmos design, but I enjoyed its playful nature just the same. Do you recognize the number pattern?

Inspired by @studymaths.bsky.social – #MathPlay 🧮 via Pascal’s Dice 🎲🔺

#ITeachMath #MTBoS #STEM #Maths #ElemMathChat #Math #MathSky #MathsToday #EduSky

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— Libo Valencia 🧮 MathPlay (@mrvalencia24.bsky.social) December 12, 2024 at 4:00 AM

Factors of 1804:

I know 1804 is divisible by four because the last two digits are divisible by 4.
1804 ÷ 4 = 451. Oh, and 4 + 1 = 5, so 451 is divisible by eleven and forty-one! Here’s a factor tree for 1804:

• 1804 is a composite number.
• Prime factorization: 1804 = 2 × 2 × 11 × 41, which can be written 1804 = 2² × 11 × 41.
• 1804 has at least one exponent greater than 1 in its prime factorization so √1804 can be simplified. Taking the factor pair from the factor pair table below with the largest square number factor, we get √1804 = (√4)(√451) = 2√451.
• The exponents in the prime factorization are 2, 1, and 1. Adding one to each exponent and multiplying, we get (2 + 1)(1 + 1)(1 + 1) = 3 × 2 × 2 = 12. Therefore, 1804 has exactly 12 factors.
• The factors of 1804 are outlined with their factor pair partners in the graphic below.

More About the number 1804:

1804 is the hypotenuse of one Pythagorean triple:
396-1760-1804, which is (9-40-41) times 44.

1804 looks interesting in some other bases:
It’s A8A in base 13 because 10(13²) + 8(13) + 10(1) = 1804.
It’s 4A4 in base 20 because 4(20²) +10(20) + 4(1) = 1804.