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Dynamically shapes change butterfly will be made by mathematics in this video. First of all we will make the approximate shape of butterfly. Observing its right wing goes up like this. And if y is equal to log x, then it goes like this. That's why we write y is equal to log x. Now this graph is below x axis, so we bring it up. To bring it up, we do 1.5 plus. As this graph goes up in the right, we need it in the left and also in the lower. That's why we will do 1.5+ Now generally, y is equal to sine x, which creates horizontal sine wave. But we will write x is equal to sine y, which will create vertical sine wave. Now we will shift it to the right by 2+ Now we will make the y axis along the reflection, here we will make mod x. Now this shape looks like a butterfly wing. But this shape is still made, it is just a 2D shape. Now to make the 3D wings of butterfly. I will write Z = X square. It looks like a parabola on the X-Z plane. But if I turn it into 3D, you see a parabolic sheet. Now we have to listen carefully. We have to draw a parabolic sheet. But we have to cut it like this that it looks like a butterfly wings. We have already found the approximate functions of butterfly wings. So if we put the function of wings in this parabolic sheet like a condition and put it less than equal to, then this sheet is drawn, but it is drawn in the bounds. Now when I put another condition and put it less than equal to, then these wings start to be drawn in our bounds. Now we multiply our parabolic sheet with sine t, which will flip the parabola. We expose its f and its amplitude from a. Now this butterfly is not complete. We will draw its body. We will draw a cylinder along its y axis. So the equation of the cylinder along the y axis will be x square plus z square is equal to k, where k is the radius of the body. But to convert this pipe into the body of the butterfly, we will have to taper it on the ends. We will have to make it smaller on the ends. To make it smaller, we multiply the radius of the cylinder by cos of y. Now it's our butterfly that will fly away. Now to cut the butterfly's body, we have put vertical sine waves and logarithm. If I put B and C constants in it and expose them as well, then by changing the values, I can change the shape of the butterfly's wings. Look at this, this is a type of butterfly, this is a type of butterfly, this is a type of butterfly, t

Dynamically shapes change butterfly will be made by mathematics in this video. First of all we will make the approximate shape of butterfly. Observing its righ…

Ideas in this flowchart

  • Mathematical Creation of Butterfly
  • 2D Butterfly Wing
  • Approximate Shape
  • Right Wing Observation
  • Graph Adjustment
  • y = log x
  • Shift Upward
  • Vertical Sine Wave
  • x = sin y
  • Shift Right
  • Reflection on y-axis
  • 3D Butterfly Wing
  • Parabolic Sheet
  • Z = X^2
  • Conditional Bounds
  • Flip Parabola
  • Body of Butterfly
  • Cylinder Along y-axis
  • x^2 + z^2 = k
  • Taper Ends
  • Adjusting Shape
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Dynamically shapes change butterfly will be made by mathematics in this video. First of all we will make the approximate shape of butterfly. Observing its right wing goes up like this. And if y is equal to log x, then it goes like this. That's why we write y is equal to log x. Now this graph is below x axis, so we bring it up. To bring it up, we do 1.5 plus. As this graph goes up in the right, we need it in the left and also in the lower. That's why we will do 1.5+ Now generally, y is equal to sine x, which creates horizontal sine wave. But we will write x is equal to sine y, which will create vertical sine wave. Now we will shift it to the right by 2+ Now we will make the y axis along the reflection, here we will make mod x. Now this shape looks like a butterfly wing. But this shape is still made, it is just a 2D shape. Now to make the 3D wings of butterfly. I will write Z = X square. It looks like a parabola on the X-Z plane. But if I turn it into 3D, you see a parabolic sheet. Now we have to listen carefully. We have to draw a parabolic sheet. But we have to cut it like this that it looks like a butterfly wings. We have already found the approximate functions of butterfly wings. So if we put the function of wings in this parabolic sheet like a condition and put it less than equal to, then this sheet is drawn, but it is drawn in the bounds. Now when I put another condition and put it less than equal to, then these wings start to be drawn in our bounds. Now we multiply our parabolic sheet with sine t, which will flip the parabola. We expose its f and its amplitude from a. Now this butterfly is not complete. We will draw its body. We will draw a cylinder along its y axis. So the equation of the cylinder along the y axis will be x square plus z square is equal to k, where k is the radius of the body. But to convert this pipe into the body of the butterfly, we will have to taper it on the ends. We will have to make it smaller on the ends. To make it smaller, we multiply the radius of the cylinder by cos of y. Now it's our butterfly that will fly away. Now to cut the butterfly's body, we have put vertical sine waves and logarithm. If I put B and C constants in it and expose them as well, then by changing the values, I can change the shape of the butterfly's wings. Look at this, this is a type of butterfly, this is a type of butterfly, this is a type of butterfly, t

"which will create vertical sine wave. Now we will shift it to the right by 2+ Now we will make the y axis along the reflection, here we will make mod x."

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