To create three different drawings showing a number of circles and triangles in which the ratio is 2:3 you can: Start with an equilateral triangle, draw a circle inside it, draw an equilateral triangle inside the circle, draw a circle in the triangle and then draw an equilateral tiangle in the smallest circle. Or, you could draw 3 triangles and 2 circles in a line. Or, you could draw 3 triangles on a line with 2 circles between them.
Yes, he created it in 459 B.C.
Semi circles cannot tessellate on their own because they do not have a consistent straight edge to fit together seamlessly without gaps or overlaps. In order to tessellate, a shape must be able to fill a plane without any overlaps or gaps. However, semi circles can be combined with other shapes to create a tessellation, such as alternating semi circles with squares or triangles.
A compass.
Two circles and a rectangle.
To create three different drawings showing a number of circles and triangles in which the ratio is 2:3 you can: Start with an equilateral triangle, draw a circle inside it, draw an equilateral triangle inside the circle, draw a circle in the triangle and then draw an equilateral tiangle in the smallest circle. Or, you could draw 3 triangles and 2 circles in a line. Or, you could draw 3 triangles on a line with 2 circles between them.
For each drawing . . .-- Draw a small number of circles.-- Draw that same number of circles again.-- Draw that same number of triangles three times.To create a different drawing, do exactly the same thing,but start out with a different small number.
Cross two match sticks to bisect like X and place the other two match sticks at the base of the two equilateral triangles formed .
Build a tetrahedron...
Yes, Euclid wrote Elements.
Create Concentric Circles.
A heptagon is a shape with 7 sides. A regular heptagon is the normal version you will see however an irregular heptagon is any shape with 7 sides.To see it visually, use the triangles to create a normal hexagon (6 sides), remove one of the triangles and put it next to one of the edges near the gap.If done correctly this will create a 7 sided object - an irregular heptagon.
A heptagon is a shape with 7 sides. A regular heptagon is the normal version you will see however an irregular heptagon is any shape with 7 sides.To see it visually, use the triangles to create a normal hexagon (6 sides), remove one of the triangles and put it next to one of the edges near the gap.If done correctly this will create a 7 sided object - an irregular heptagon.
One way to do this problem is as follows: Let X represent the area of the overlap (which we know is 20000. Let S represent the area in one circle that is outside of the overlapping area (it is best to draw yourself a picture). Because the circles are identical, there is a symmetry such that the S is the same in each circle. Now create a two equilateral triangles with sides of length r in the overlap, one going up and one going down. If you draw the figure correctly, in the overlap portion will comprise the two equilateral triangles, as well as four identical regions outside the triangles but in the overlap. Let Y represent the area of each of those regions. The area of each of the equilateral triangles is (sqrt(3)/4)*r2 (For an equilateral triangle the height is (sqrt(3)/2) times the length of one of the sides, which can be found using the Pythagorean theorem and observing that the base of a right triangle is half the length of a side, and they hypotenuse is the length of the side.) Now, for two equations that can be solved to find the radius, r: 1. As mentioned above, the overlapping portion comprises the two equilateral triangles that I mentioned plus the four additional regions, each with area Y. Thus, 4Y+((sqrt(3)/4)(r^2)*2=20000 2. In addition, consider the 120 degree sector in one of the circles that comprises the two triangles and two of the regions with area Y. 120 degrees is one third of a circle, so the area of this sector is (1/3)*pi*r^2. Thus, 2Y+((sqrt(3)/4)(r^2)*2= (1/3)*pi*(r^2) Now you have two equations and two unknowns. Solving for r, yields: r=sqrt((20000/((2/3)*pi-(sqrt(3))/2), which equals about 127.6 cm.
Yes, he created it in 459 B.C.
Semi circles cannot tessellate on their own because they do not have a consistent straight edge to fit together seamlessly without gaps or overlaps. In order to tessellate, a shape must be able to fill a plane without any overlaps or gaps. However, semi circles can be combined with other shapes to create a tessellation, such as alternating semi circles with squares or triangles.
Each angle in an equilateral triangle is 60 degrees. In order to create a regular tessellation of an area, we need for the angles of the polygons we are putting near each other to sum to 360 degrees. If you place six equilateral triangles so that all of them share a vertex, and each triangle is adjacent to two others, you get 60*6 = 360 degrees in that vertex. Please see related link for a demo of a triangular tessellation.