We have seen in the previous post the patterns made by the the tangents of certain parametric lines. This is a follow-up on that post and we will look at the same closed figures by plotting normals to them.

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#### Introduction:

Definition: The simplest description of a normal is that it is a line segment perpendicular to the curve or the surface at the point where it is rooted. This is the Wikipedia link.

Calculation:

If you have a two-dimensional curve defined by the parametric equations *x = x(t)* and *y = y(t)*

The general equation for the normal at any point of such curve would be *N _{x}(t) = x”(t) and N_{y}(t) = y”(t)*

Example:

- Parametric Equation of a circle is x = x(t) = +Sin(t) and y = y(t) = +Cos(t);
- Tangent at any point is T
_{x}(t) = x'(t) = +Cos(t) and Ty(t) = y'(t) = -Sin(t); - Normal at any point is N
_{x}(t) = x”(t) = -Sin(t) and N_{y}(t) = y”(t) = -Cos(t);

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*Note 1* In this series, there will not be a separate image for the curve and the normals. The curve will be a closed line and it will be conspicuous enough to be visually separable from the other lines.

*Note 2* This is also the longest post till date of the fermibot blog.

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#### Three lobes

1. 400 Normals

2. 1000 Normals

3. 4000 Normals

#### Four Lobes

1. 400 Normals

2. 1000 Normals

3. 4000 Normals

#### Five Lobes

1. 400 Normals

2. 1000 Normals

3. 4000 Normals

#### 6 Lobes

In this case, the normals were too long. So, I have shortened them, to show the details of the center.

1. 400 Normals

2. 1000 Normals

3. 4000 Normals

#### Bonus 1 (5 Lobes Version 2)

1. 200 Normals

2. 400 Normals

3. 4000 Normals

#### Bonus 2 (6 Lobes Version 2)

1. 200 Normals

2. 400 Normals

3. 4000 Normals

#### Bonus 3 (Bi-Color Flora)

- For one curve, both the tangent and the Normals are shown at the same time
- Notice the alignment and the striking symmetry of the objects.

1. 200 Normals + 200 Tangents

2. 2000 Normals + 2000 Tangents

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