Mathematics in the Modern World - Sequences and Recreational Mathematics

This set of vocabulary flashcards covers essential definitions regarding mathematical sequences, difference tables, and specific concepts in recreational mathematics as discussed in the GE013 course.

Infinite sequence

A function whose domain is the set of positive integers.

Finite sequence

A sequence where the domain of the function consists of the first positive integers only.

Terms of the sequence

The function values denoted as $1, 2, 3, …, (n-1), n, …$.

General term

The $n$-th term of a sequence, often represented as $a_n$.

Difference table

A table showing the difference between successive terms of a sequence, which can include first, second, and third differences to predict the next term.

Recreational Mathematics

A mathematical activity involving mathematical problems and games, such as magic squares, logic puzzles, and culture mathematics.

Lo Shu

A Chinese magic square pattern of order $3$ found on the shell of a sacred turtle during the time of Emperor Yu.

Durer’s Melancholia

A $1514$ engraving by artist Albrecht Durer that contains a magic square pattern of order $4$.

Palindrome

A number, word, or phrase sequence of characters that reads the same backward as forward, such as $131$ or $12321$.

Plateau Primes

A type of palindromic prime, with examples included in the transcript such as $18888881$ and $199999991$.

Smoothly Undulating

A type of palindrome sequence such as $323232323$ or $727272727$.

Peak Primes

A type of palindromic prime where the digits increase and then decrease, such as $123494321$.

Valley Primes

A type of palindromic prime such as $111191111$ and $777767777$.

Pascal’s Triangle

A mathematical triangle named after Blaise Pascal ($1623-1662$), though it was described by earlier Chinese mathematicians.

Zhu Shijie

A Chinese mathematician ($1260-1320$) who published the triangle now known as Pascal's Triangle in his $1303$ work ‘Si Yuan Yu Jian’.

Jia Xian Triangle

One of the Chinese names for the triangle published by Zhu Shijie, also known as the Yanghui Triangle.