1128 can refer either to the natural number that follows 1127 and precedes 1129 or to the calendar year AD 1128 in the High Middle Ages. As a numeral it appears in arithmetic, combinatorics and numeral systems; as a year it falls within a period of dynastic rivalries and territorial consolidation in western Europe.

Mathematical characteristics

As an integer, 1128 is an even composite number. Its prime factorization is 2^3 × 3 × 47. It is an abundant number because the sum of its proper divisors (1, 2, 3, 4, 6, 8, 12, 16, 24, 47, 48, 47×2=94, etc.) exceeds the number itself. In combinatorial terms, 1128 equals the binomial coefficient "48 choose 2" (48·47/2), and it is the 47th triangular number (the sum of the integers 1 through 47). In Roman numerals it is written as MCXXVIII.

Year 1128 (AD): historical context

The year 1128 belongs to the High Middle Ages, a period marked by growing feudal states, church reform, and expanding monastic influence across Europe. In the political landscape of western Europe, succession, marriage alliances and regional conflicts shaped the next generations of rulers.

Notable events (examples)

  • Battle of São Mamede (1128): Fought near Guimarães in the northwest Iberian Peninsula, this clash is commonly regarded as a turning point in the emergence of the County of Portugal. The conflict strengthened the position of Afonso Henriques, who would later be recognized as the first king of Portugal.
  • Marriage of Empress Matilda (1128): Empress Matilda, daughter of King Henry I of England, married Geoffrey of Anjou in 1128. This union linked the Norman-English and Angevin houses and had long-term consequences for English and French dynastic politics.

Other occurrences in 1128 included routine ecclesiastical and regional developments typical of the era: local lordships consolidating power, monastic foundations, and diplomatic marriages. In calendrical terms, 1128 was a leap year in the Julian calendar.

Because "1128" can denote either a mathematical object or a date, discussions of it appear in diverse contexts—from number theory and combinatorics to medieval history and genealogy. Its mathematical facts (factorization, triangular form, binomial appearance) are straightforward and commonly used, while the historical references are usually invoked when tracing the origins of states and dynastic lines in twelfth-century Europe.