Isometries are transformations that don't affect the size and shape of an option. Think sliding, rotating, mirroring. Also think about dinosaurs on flying translation carpets next to reflected rawrs and rotated cheese.
I can't believe how much dopamine learning geometry is sparking. Covered Isometries tonight, and got to draw a dinosaur on a flying isometry carpet, with it's rawr reflected next to rotated cheese, ahem, triangles.
An isometry is a transformation, like changing the position, orientation, rotating, flipping, moving an object without changing the shape or size of it. An isometry (transformation) preserves the distances between points and angles between lines and shapes. Which is the more confusing way of saying the shape is moved without being changed.
Three transformations were covered in the intro to Euclidean geometry vocab section:
Where you flip a shape over a line of reflection, like a mirror. Every point on the object moves to a new location directly opposite (perpendicular) on the other side of the line, at an equal distance.
Ref1(object)
Ref means Reflection.
1 means the line of reflection.
object being the thing that is being reflected.
Where an object is moved from one location to another, without rotating, flipping or changing size. It can move both left and right and up and down along the x and y coordinates.
A question that came to mind was: What about diagonal movement.
Diagonal movement is caused when you move the shape vertically AND horizontally at the same time.
f(x,y) = (a + x, b + y)
f means function, and the x and y are the original coordinates of the shape on both the x (horizontal) and y (vertical) axis. They are passed into the function.
a is the amount the object is moved along the x axis (left or right, a minus or positive value), and b is the same but for the y axis (up and down).
I'm a bit confused by the way the formula is written. I don't have a math background, I have a programming background, so the function part makes sense, but the = followed by the parenthesis part doesn't. I know what it all means individually, but I don't get why it's written like that, instead of just tran(a + x, b + y).
Guessing this is a convention that'll make more sense with exposure to different types.
Rotation is where you rotate an object around a point by an angle of a certain size. The point can be anywhere, it can be inside the shape, on the edge, or anywhere outside of it. In all cases, it's like sticking a drawing pin in a piece of paper and rotating the paper around the pin.
That's actually a helpful visualisation I should add a sketch of it.
Rot(P, 0, object)
I wonder how people actually write formulas on math blogs, that's another thing to figure out.
Rot means rotation,
P is the point of rotation (I imagine it as x,y coordinates, so wonder what the numerical representation of the point value would be).
0 is the angle of rotation (0 - 360), and object is the thing being rotated.
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It's nearly midnight and I want to fill in the next section instead of sleep. Don't dooo it.