Awakening the Mathematical Brain

  • Home
  • About
  • People
  • Math brain
  • Awakening
  • Examples
    • Positive
  • Stories
  • Questions
  • Mathematical issues
    • Writing
    • Proof
  • Bibliography
en English
af Afrikaanssq Albanianam Amharicar Arabichy Armenianaz Azerbaijanieu Basquebe Belarusianbn Bengalibs Bosnianbg Bulgarianca Catalanceb Cebuanony Chichewazh-CN Chinese (Simplified)zh-TW Chinese (Traditional)co Corsicanhr Croatiancs Czechda Danishnl Dutchen Englisheo Esperantoet Estoniantl Filipinofi Finnishfr Frenchfy Frisiangl Galicianka Georgiande Germanel Greekgu Gujaratiht Haitian Creoleha Hausahaw Hawaiianiw Hebrewhi Hindihmn Hmonghu Hungarianis Icelandicig Igboid Indonesianga Irishit Italianja Japanesejw Javanesekn Kannadakk Kazakhkm Khmerko Koreanku Kurdish (Kurmanji)ky Kyrgyzlo Laola Latinlv Latvianlt Lithuanianlb Luxembourgishmk Macedonianmg Malagasyms Malayml Malayalammt Maltesemi Maorimr Marathimn Mongolianmy Myanmar (Burmese)ne Nepalino Norwegianps Pashtofa Persianpl Polishpt Portuguesepa Punjabiro Romanianru Russiansm Samoangd Scottish Gaelicsr Serbianst Sesothosn Shonasd Sindhisi Sinhalask Slovaksl Slovenianso Somalies Spanishsu Sudanesesw Swahilisv Swedishtg Tajikta Tamilte Teluguth Thaitr Turkishuk Ukrainianur Urduuz Uzbekvi Vietnamesecy Welshxh Xhosayi Yiddishyo Yorubazu Zulu

The dorsolareral prefrontal cortex is activated in expert mathematician's brains when intepreting mathematical statments.

 

This brain region is associated with, but not exclusively responsible for, executive functions, including working memory, cognitive flexibility planning, inhibition, and abstract reasoning.

Diagonals of a square array

The 5 \times 5 array

contains 5^2 = 25 dots, arranged in 5 rows and 5 columns.

We can view the array as consisting of a series of disjoint diagonals:

Counting the dots in the diagonals we get

(1+2+3+4)+5+(4+3+2+1) = 5\times 5

which, looked at another way, says

1+2+3+4 = (5^2-5)/2 .

Of course, there’s nothing special about 5: we can see by looking at an 11\times 11 square array of dots that

1+2+\ldots + 9 +10 = (11^2-11)/2

and, more generally, if n is any positive integer then

1+2+\ldots + n-2 +n-1 = (n^2-n)/2 .

Seeing a square array of dots as a series of diagonals is key to understanding, and proving, that

1+2+\ldots + n-2 +n-1 = (n^2-n)/2

for any positive integer n .

This idea is a small, yet significant, step in awakening a developing mathematical brain.

 

Leave a Reply Cancel reply

© 2019 Republic of MathematicsTM & Krackle LLC