1. Get numbers of phi
The quadrature problem is the computation of phi, the ratio of the circumference of a circle to its diameter. We have seen that in the ancient orient the value of phi was frequently taken as three and for the Egyptian quadrature of the circle given in the Rhind papyrus, we have phi equals to three point one six. The first scientific attempt to compute phi, seems to be that of Archimedes with his achievement. To simplify matters, suppose we choose a circle with unit diameter. Now the (length of the) circumference of a circle lies between the perimeter of any inscribed polygon and that of any circumscribed polygon. According Archimedes, phi is between twenty two seventh or in decimal places, phi is given by three point fourteen. In the work are found same remarkable rational approximations to irrational square roots. The method of computing phi by using regular inscribed and circumscribed polygon is known as the classical method of computing phi. Except Archimedes, still more scientist attempt to compute the value of phi.
2. Get the formula of ABC
• Change all of segment to be a coefficient x
• Eliminate Constanta of left segment or both of joint minus with c/a
• Add both of joint with a half of quadrature from coefficient x
• Change the left join to be a complete quadratic
3. Find out the area
There are two lines equation. So, to find out the region bounded is the first lines equation should be equals to the second lines equation or y1=y2. After that, we will get the value of x. the value of x is the region bounded. Then to find out the area, we use the formula of integration with the region bounded among negative one until two. After calculate it, we will get result is negative thirteen sixth unit of area.
4. To decided the volume of cone
Cone is pyramid that have base plane curved circle. The volume of cone equals to the volume of pyramid. If known a cone with base radius r and altitude t, then to find the volume of cone equals to one third from the base’s area times the altitude. The base’s area equals to phi times the quadrature of radius. Thus, the volume of cone is one third from phi times the quadrature of radius times cone’s altitude.
5. To prove that in immaterial triangle then the totally of angel is one hundred eighty degree
The first, we make an immaterial triangle then make stretch of lines from point everywhere. For example, point of C collinear with AC. Then, exceed the point of C; make lines that parallel with AB. The angle of DCE equals to the angle of CAB because it’s opposite each other. The angle of BCE equals to the angle of ABC because it’s on both sides. The angle of ACB plus the angle of BCE plus the angle of ECD lie in one line equals to one hundred eighty degree, so the angle of ACB plus the angle of ABC plus the angle of CAB equals to one hundred eighty degree is proved.
6. To decided probability appear sum of figure more than six from two dices threw entirely
To make easier us to find out probability with make a table of probability. If there are two dices, then it has thirty six sample spaces. Whereas the probability appear two dices is twenty one. Thus, the probability appear figure more than six is twenty one over thirty six.
7. To decided the lines equation exceedingly (10,0) and tangent of circle
We should find the value of gradient. To find it, we should make equation inform Ax+By+C=0. To get equation like that, we should use roots of the equation known and the equation should be equals to zero. After that, to find the gradient, we use the formula is m= . So, the line equation also use the formula, the formula is . For the value of x and y, we used exceed point is ten and zero. Ten as x and zero as y. The equation can inform y equals to or the lines equation equals to zero.
8. To prove the theorem of Pythagoras
The Pythagorean Theorem only used for right triangle. In a right triangle, with sides a and b, and hypotenuse c, then power of c equals to power of a plus power of b. A right triangle is a triangle with one right angle has an angel ninety degree. And sides a and b perpendicular mutually. The simplest proof is an algebraic proof using similar triangles. Similar triangle has proportional sides.
9. To find out the sum of odd numbers two hundred first
With use arithmetic series, first term is one, with difference is two and there are one hundred terms. Then, sum of odd numbers two hundred first equals to a half times one hundred multiple two times the first term plus the hundred terms minus one times two, the answer equals to ten thousand.
10. Paint or make the cube that known lateral edges
For example, we will make the cube ABCDEFGH, the base ABCD and vertical lateral edges AE, BF, CG, and DH. With the length of lateral edges is six cm, the angle is thirty degree and the proportion projection is two over five. The steps:
• Design line of AB along six cm horizontal
• At point of A, paint the angle thirty degree, AD is segment orthogonal line because the length of projection two over five, then the length of AD equals to two cm
• Gradient projection of square ABCD shaped parallelogram, then the base can solve
• The middle of lateral edges shaped vertical line segment, so that the point of angle E, F, G, H can draw, and then produced the cube ABCDEFGH