My topic for inquiry project was about golden ratio.
The main question was “How Does Golden Ratio Work in Math and Art?”
Further questions: In what ways will golden ratio benefit our future?
Why do we use golden ratio for smartphones, t.v.s, credit cards, and more? Can’t it be another ratio?
In math class, we used desmos to graph Santa face. We learned about different types of graphs such as linear function, quadratic function, cubic function, square root function, absolute value function, and rational function. I used the relation, x²+y²=6 to make the face of Santa, Relations (x-0.9)²+(y-0.7)²≤0.1 and (x+0.9)²+(y-0.7)²≤0.1 to make eyes. x²+(y+0.3)²≤0.2 for the nose. I used function, the parabola y=-2x²+9 {xl x∈R, -1.9≤x≤1.9} for Santa hat. Relation, the circular equation x²+(y-9.6)²=0.5 for the round shape on top of the hat. I used function, parabola y=0.2x²-1.2 {xl x∈R, -2.5≤x≤2.5} to draw the top part of Santa’s beard and bottom for y=0.8x²-5 {xl y∈R, y≤0}. At last to draw mouth, I used the basic function y=-1.4 {xl x∈R, -1.2≤x≤1.2}
I mostly used circular equation x²+y²=4, to move the center of circle (0,0) to 2 to right and 2 to up. I would use the equation (x-2)²+(y-2)²=4.
ex) (2x+1)(x+2)=?
(2x+1)(x+2)= 2x^2+5x+2
I used the method FOIL in the distributive property.
(a+b)(c+d)= ab+ad+bc+bd
2. How to factor a trinomial Support your work with algebra
ex) (x+1)(x+2)(x+3)=?
(x^2+3x+2)(x+3)
=x^3+3x^2+3x^2+9x+6
=x^3+6x^2+9x+6
First I started with (x+1)(x+2) and expand it, then I multiplied x^2+3x+2 and (x+3)
In math class, I used an orange to find out the surface area of a sphere.
By cutting the peals of an orange and placed them in a circle. It was an interesting way to solve the surface area of a sphere.
The formula of sphere’s surface area is 4πr.
The first unit was about numbers. In specific there was prime numbers, radicals, and number system. In prime number section, we have learned that prime numbers are numbers which is one and itself. We would do prime factorization to figure out the factors and determine if it was a prime number or not. The next section was about radicals, we learned about changing the whole radical to mixed radical and mixed radical to whole radical. Also, we have learned about square root and cube root. Last thing is about the real number system. In real number system, numbers can be divided to rational and irrational. In irrational, there would be roots and pi. When you describe it in a diagram, there will be few sets of numbers included as rational : integers, whole numbers, and natural numbers.