# 1164 Mathematics at Corvin Castle

In the forests of Transylvania in what is now Hunedoara, Romania, a large, beautiful, well-restored, and fascinating castle awaits. At Corvin Castle, you can see how enemies were tortured and royal friends were entertained in the days of kings and knights. However, the room that intrigued me the most was full of mathematics. I didn’t take a picture of every geometric shape that graced its walls; I only took a few. You will have to go there yourself to see all the wonderful mathematical artwork. I thoroughly enjoyed myself!

I knew that fellow mathematical puzzle maker, Simona Prilogan,  was from Romania, but I didn’t realize until after I returned home that this castle is in her hometown! She recently wrote about the castle and her experience growing up in Hunedoara. As a child, she was chosen to write a poem about Romania’s president and present the poem at this very castle.

Now I’ll tell you a little something about the number 1164:

• 1164 is a composite number.
• Prime factorization: 1164 = 2 × 2 × 3 × 97, which can be written 1164 = 2² × 3 × 97
• The exponents in the prime factorization are 2, 1, and 1. Adding one to each and multiplying we get (2 + 1)(1 + 1)(1 + 1) = 3 × 2 × 2 = 12. Therefore 1164 has exactly 12 factors.
• Factors of 1164: 1, 2, 3, 4, 6, 12, 97, 194, 291, 388, 582, 1164
• Factor pairs: 1164 = 1 × 1164, 2 × 582, 3 × 388, 4 × 291, 6 × 194, or 12 × 97
• Taking the factor pair with the largest square number factor, we get √1164 = (√4)(√291) = 2√291 ≈ 34.117444

1164 is the sum of consecutive prime numbers FOUR different ways:
It’s the sum of the eighteen prime numbers from 29 to 103.
97 + 101 + 103 + 107 + 109 + 113 + 127 + 131+ 137 + 139 = 1164; that’s ten consecutive primes,
281 + 283 + 293 + 307 = 1164; that’s four consecutive primes, and
577 + 587 = 1164; that’s two consecutive primes.

1164 is the hypotenuse of a Pythagorean triple:
780-864-1164 which is 12 times (65-72-97)

1164 is palindrome 969 in BASE 11 because 9(11²) + 6(11) + 9(1) = 1164,
and it’s 345 in BASE 19 because 3(19²) + 4(19) + 5(1) = 1164

## 4 thoughts on “1164 Mathematics at Corvin Castle”

1. Looks like an amazing castle. We were in Romania last month and visited quite a few places, including Bran Castle, but Corvin was a bit too far to reach. Romania is a very beautiful country.

• ivasallay

Yes, Romania is quite beautiful, however, being driven through the winding mountains of Transylvania made me a little nervous even though the scenery was breathtaking. When the motorway is completed, the trip will be much quicker and easier. We were there in June from the 25th to the 28th. I wonder if we were there at the same time that you were?

• We arrived about a week after you left. I know what you mean about the winding roads. The new motorways were very fast, but a few times we ventured away from the main roads and very quickly found ourselves on little more than dirt tracks. Twice we decided to turn the car around because the road surface simply deteriorated to rocks and dirt.

2. I after I read the 120th Playful Math Carnival I had to search for your post about the castle. I am so happy you enjoyed your stay there. I will add this castle on my “must see places to visit” when I go back home next summer. Great article.

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