Table of Contents
Who invented the triangular number?
It is named for the 17th-century French mathematician Blaise Pascal, but it is far older. Chinese mathematician Jia Xian devised a triangular representation for the coefficients in the 11th century.
When was triangular numbers invented?
However, regardless of the truth of this story, Gauss was not the first to discover this formula, and some find it likely that its origin goes back to the Pythagoreans in the 5th century BC. The two formulas were described by the Irish monk Dicuil in about 816 in his Computus.
How is a triangular number calculated?
About Triangular Numbers Triangular numbers are a pattern of numbers that form equilateral triangles. The formula for calculating the nth triangular number is: T = (n)(n + 1) / 2.
How is 666 a triangular number?
In mathematics + 34 + 35 + 36 = 666), and thus it is a triangular number. Because 36 is also triangular, 666 is a doubly triangular number. Also, 36 = 15 + 21; 15 and 21 are also triangular numbers, and 152 + 212 = 225 + 441 = 666.
How was Pascal’s Triangle discovered?
The triangle was first seen in Europe in 1527 when Petrus Apianus featured it on his frontispiece in his book about business calculations. They actually call the triangle Tartagalia’s Triangle in Italy, named after the Italian Algebraist Niccolo Fontana Tartagalia. He published six rows of the triangle in 1556.
Where did Pascal’s triangle originated?
Pascal’s triangle was known in China in the early 11th century through the work of the Chinese mathematician Jia Xian (1010–1070). In the 13th century, Yang Hui (1238–1298) presented the triangle and hence it is still called Yang Hui’s triangle (杨辉三角; 楊輝三角) in China.
What is the history of triangle?
The triangle was known by the 14th century and was sometimes trapezoidal in form; until about 1800 it often had jingling rings. With cymbals and bass drums, triangles were basic to the Turkish Janissary music in vogue in 18th-century Europe, entering the orchestra at that time as a device for local colour.
Why do we learn triangular numbers?
Triangular numbers provide many wonderful contexts for mathematical thinking and problem solving. Triangular numbers are figurate numbers because they represent counting numbers as a geometric configu- ration of equally spaced points.
Which is the first triangular number?
The triangular number sequence is the representation of the numbers in the form of equilateral triangle arranged in a series or sequence. These numbers are in a sequence of 1, 3, 6, 10, 15, 21, 28, 36, 45, and so on.
Is 1711 a triangle number?
1711 is the 58th Triangular Number because (58·59)/2 = 1711.
Why do we need triangular numbers?
One of the main reasons triangular numbers are important in mathematics is because of their close relationship to other number patterns. For example, square numbers, as well as cube numbers and other geometric figures, follow a similar formula to that which is used when calculating triangular numbers.
Is zero a triangular number?
List Of Triangular Numbers. 0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 105, 120,136, 153, 171, 190, 210, 231, 253, 276, 300, 325, 351, 378, 406, 435, 465, 496, 528, 561, 595, 630, 666, 703, 741, 780, 820, 861, 903, 946, 990, 1035, 1081, 1128, 1176, 1225, 1275, 1326, 1378, 1431, and so on.
Who invented Pascal’s Triangle in India?
It was also realised that the shallow diagonals of the triangle sum to the Fibonacci numbers. The Indian mathematician Bhattotpala (c. 1068) later gives rows 0-16 of the triangle.
Who is the father of Pascal’s triangle?
In Italy, Pascal’s triangle is referred to as Tartaglia’s triangle, named for the Italian algebraist Niccolò Fontana Tartaglia (1500–1577), who published six rows of the triangle in 1556. Gerolamo Cardano, also, published the triangle as well as the additive and multiplicative rules for constructing it in 1570.
Did Blaise Pascal invent the triangle?
Pascal’s Triangle is a special triangular arrangement of numbers used in many areas of mathematics. It is named after the famous 17 th century French mathematician Blaise Pascal because he developed so many of the triangle’s properties.
What is a triangular number?
Triangular numbers are a type of figurate number, other examples being square numbers and cube numbers. The n th triangular number is the number of dots in the triangular arrangement with n dots on each side, and is equal to the sum of the n natural numbers from 1 to n.
How to find the nth triagular number?
The nth triangle number is the number of dots composing a triangle with n dots on a side, and is equal to the sum of the n natural numbers from 1 to n. The general representation of a triangular number is where n is a natural number. This sum is Tn = n * (n + 1) / 2. This is the triangular number formula to find the nth triagular number.
Who invented the calculating machine?
An improvement in Schickard’s design, it nevertheless suffered from mechanical shortcomings and higher functions required repetitive entries. William Seward Burroughs (1857-1898): In 1885, Burroughs filed his first patent for a calculating machine. However, his 1892 patent was for an improved calculating machine with an added printer.
What is the sum of the first n triangular numbers?
The sum of the first n triangular numbers is the n th tetrahedral number : ∑ k = 1 n T k = ∑ k = 1 n k ( k + 1 ) 2 = n ( n + 1 ) ( n + 2 ) 6 . {\\displaystyle \\sum _ {k=1}^ {n}T_ {k}=\\sum _ {k=1}^ {n} {\\frac {k (k+1)} {2}}= {\\frac {n (n+1) (n+2)} {6}}.}