Sertyujk,
STELLAR NUMBERS
Introduction:
Stellar numbers are sequence of numbers that follow a certain pattern, when we plot it into a diagram it will create a geometrical star-like shape. Each stellar number has its own vertices and number of dots, the formula will be different for every vertices. We are now going to determine the number of dots in each stage, and then we could see the pattern of the number of dots. Finally, we can generate a simplified formula or general statement for to find the number of dots in each stage.
Triangular numbers are sequence of number that has certain pattern and if we plot it into a diagram it will create a geometrical triangular shape. Each triangular number has its own number of dots and formula. Now, we will start with triangular number first.
Aim: In this task I will consider geometric shapes which lead to special numbers. The simplest example of these are square numbers, 1,4,9,16 which can be represented by squares of side 1,2,3 and 4.
The following diagrams show a triangular pattern of evenly spaced dots. The numbers of dots in each diagram are examples of triangular number (1,3,6,...).
[pic] [pic] [pic][pic]
1 3 6 10 15
Complete the triangular numbers sequence with three more terms.
[pic] [pic] [pic]
21 28 36
S6 = 21 dots
S7= 28 dots
S8 = 36 dots
General statement that represents the nth triangular number in terms of n
Sn = 1/2n2 + 1/2n
Consider stellar (star) shapes with p vertices, leading to p-stellar numbers. The firsr four representations for a star with six vertices are shown in the four stages S1-S4 below. The 6-stellar number at each stage is the total number of dots in the diagram.
[pic] [pic] [pic]
S1
Introduction:
Stellar numbers are sequence of numbers that follow a certain pattern, when we plot it into a diagram it will create a geometrical star-like shape. Each stellar number has its own vertices and number of dots, the formula will be different for every vertices. We are now going to determine the number of dots in each stage, and then we could see the pattern of the number of dots. Finally, we can generate a simplified formula or general statement for to find the number of dots in each stage.
Triangular numbers are sequence of number that has certain pattern and if we plot it into a diagram it will create a geometrical triangular shape. Each triangular number has its own number of dots and formula. Now, we will start with triangular number first.
Aim: In this task I will consider geometric shapes which lead to special numbers. The simplest example of these are square numbers, 1,4,9,16 which can be represented by squares of side 1,2,3 and 4.
The following diagrams show a triangular pattern of evenly spaced dots. The numbers of dots in each diagram are examples of triangular number (1,3,6,...).
[pic] [pic] [pic][pic]
1 3 6 10 15
Complete the triangular numbers sequence with three more terms.
[pic] [pic] [pic]
21 28 36
S6 = 21 dots
S7= 28 dots
S8 = 36 dots
General statement that represents the nth triangular number in terms of n
Sn = 1/2n2 + 1/2n
Consider stellar (star) shapes with p vertices, leading to p-stellar numbers. The firsr four representations for a star with six vertices are shown in the four stages S1-S4 below. The 6-stellar number at each stage is the total number of dots in the diagram.
[pic] [pic] [pic]
S1