{"id":28063,"date":"2024-05-22T16:25:46","date_gmt":"2024-05-22T21:25:46","guid":{"rendered":"https:\/\/www.wlbott.com\/?p=28063"},"modified":"2024-05-22T17:04:14","modified_gmt":"2024-05-22T22:04:14","slug":"centered-square-number","status":"publish","type":"post","link":"https:\/\/www.wlbott.com\/?p=28063","title":{"rendered":"Centered Square Number"},"content":{"rendered":"\n

Let’s talk a little more about 41….<\/p>\n\n\n\n

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WLBOTT:<\/strong> Yesterday two Elders <\/strong>of WLBOTT <\/strong>celebrated their 41st<\/sup> wedding anniversary (to each other<\/em>). Can you tell me some special properties for the number 41?<\/p>\n<\/blockquote>\n\n\n\n

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Chat:<\/strong> Congratulations on the Elders’ 41st wedding anniversary! That’s a wonderful milestone. Here are some interesting properties and facts about the number 41<\/strong>:<\/p>\n\n\n\n

**Prime Number**:<\/strong> 41 is a prime number, meaning it is only divisible by 1 and itself. It is the 13th prime number.<\/p>\n\n\n\n

**Centered Square Number**:<\/strong> 41 is a centered square number, which means it can be represented as a square with a dot in the center and other dots around it forming concentric squares. The formula for the ( n )-th centered square number is ( n2<\/sup> + (n-1)2<\/sup> ). For ( n = 5 ), the result is 41.<\/p>\n\n\n\n

**Sum of Three Squares**:<\/strong> 41 can be expressed as the sum of three squares in multiple ways:<\/p>\n\n\n\n

( 41 = 42<\/sup> + 22<\/sup> + 12<\/sup> )<\/p>\n\n\n\n

( 41 = 52<\/sup> + 22<\/sup> + 02<\/sup> )<\/p>\n\n\n\n

**Euler’s Lucky Number**:<\/strong> Euler discovered that the quadratic polynomial ( n2<\/sup> + n + 41 ) produces prime numbers for ( n ) from 0 to 39. This sequence of primes is often referred to as Euler’s lucky numbers.<\/p>\n\n\n\n

**Hexagonal Number**:<\/strong> 41 is a centered hexagonal number, which means it can be visualized as a hexagon with a central dot and layers of dots surrounding it in hexagonal patterns.<\/p>\n\n\n\n

**Sum of First Six Prime Numbers**:<\/strong> The sum of the first six prime numbers (2, 3, 5, 7, 11, and 13) is 41.<\/p>\n\n\n\n

These properties show that 41 is quite an interesting number with various mathematical and cultural significance. Happy anniversary again!<\/em><\/p>\n<\/blockquote>\n\n\n\n

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41: Centered Square Number<\/h3>\n\n\n\n
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In elementary number theory, a centered square number is a centered figurate number that gives the number of dots in a square with a dot in the center and all other dots surrounding the center dot in successive square layers. That is, each centered square number equals the number of dots within a given city block distance of the center dot on a regular square lattice. While centered square numbers, like figurate numbers in general, have few if any direct practical applications<\/span><\/em>[1]<\/sup>, they are sometimes studied in recreational mathematics for their elegant geometric and arithmetic properties.<\/p>\n\n\n\n

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[1]<\/sup> “few if any direct practical applications<\/span><\/em>“; i.e. WLBOTT<\/p>\n\n\n\n

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Quadrinia<\/h3>\n\n\n\n

Quadrinia <\/strong>– The WLBOTT <\/strong>Goddess and Protectoress of the number 41 (XLI), square roots, prime numbers under 101, and hard drive archives.<\/p>\n\n\n\n

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Centrovia<\/h3>\n\n\n\n

Centrovia<\/strong> – The WLBOTT<\/strong> Goddess and Protectoress of Moderation, pickled herring, carbon sequestration, and hexagonals.<\/p>\n\n\n\n

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Closenufeous (Greek) \/ Approximodus (Roman)<\/h3>\n\n\n\n

Closenufeous<\/strong> (Greek) \/ Approximodus<\/strong> (Roman) – The WLBOTT <\/strong>Trickster God of Almost Primes, Approximations, Dollar Cost Averaging, and Just-in-Time Manufacturing.<\/p>\n\n\n\n

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Empress Decimalina Digitina<\/strong><\/strong><\/h3>\n\n\n\n

Decimalina Digitina<\/strong><\/strong> is the fairy queen of rounding errors, and an angry queen is she.<\/p>\n\n\n\n

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Let’s talk a little more about 41…. WLBOTT: Yesterday two Elders of WLBOTT celebrated their 41st wedding anniversary (to each other). Can you tell me some special properties for the number 41? Chat: Congratulations on the Elders’ 41st wedding anniversary! That’s a wonderful milestone. Here are some interesting properties and facts about the number 41: […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"nf_dc_page":"","_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_feature_clip_id":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_post_was_ever_published":false},"categories":[82,32],"tags":[],"class_list":["post-28063","post","type-post","status-publish","format-standard","hentry","category-erudition","category-mildly-interesting"],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/www.wlbott.com\/index.php?rest_route=\/wp\/v2\/posts\/28063","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.wlbott.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.wlbott.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.wlbott.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.wlbott.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=28063"}],"version-history":[{"count":5,"href":"https:\/\/www.wlbott.com\/index.php?rest_route=\/wp\/v2\/posts\/28063\/revisions"}],"predecessor-version":[{"id":28114,"href":"https:\/\/www.wlbott.com\/index.php?rest_route=\/wp\/v2\/posts\/28063\/revisions\/28114"}],"wp:attachment":[{"href":"https:\/\/www.wlbott.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=28063"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.wlbott.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=28063"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.wlbott.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=28063"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}