similarity - Ähnlichkeit

similar shapes - ähnliche Figuren

introduction

what is similarity?

task 1

What shapes are similar?

TODO - page with similar shapes.

What can you say about the angles when they are similar?

What can you say about the ratios of matching sides to each other?

task 2 - a tree and its shadow.

How can we determine the height of a tree with just a measuring tape?

hints sideimage

similarity - Ähnlichkeit

task enlarge a drawing

Let’s say you want to enlarge a drawing that is on square paper.

sideimage sideimage sideimage make your own drawing.

stretch factor (enlargement factor) - Ähnlichkeitsfaktor

If two shapes A and B are similar, we write $A \sim B$.

$\frac{1}{4}$, 25 %, 1 : 4 and 0.25 mean the same scale factor

enlargement / reduction - zentrische Streckung

experiment

materials

procedure

make sure the knot follows the curve you want to enlarge. Keep the pin and paper fixed.

video

here is a link to a video demonstration

Extension: - What happens if the knot is not halfway?

theory

Note: always measure from point Z.

The shapes are similar. Die Figuren sind ähnlich.

Strahlensätze

1. Strahlensatz

$${\frac{a_1}{a_2} = \frac{b_1}{b_2}}$$

2. Strahlensatz

$${\frac{a_1}{a_2} = \frac{c_1}{c_2}}$$ and $${\frac{b_1}{b_2} = \frac{c_1}{c_2}}$$

ratios of lengths - Verhältnisse der Längen

$${l_{image} = l_{original} \cdot k}$$

what about the area of shapes?

example - rectangle - ${A = a \cdot b}$

image: ${A' = (ak) \cdot (bk) = a \cdot b \cdot k \cdot k = ab \cdot k^2 = A \cdot k^2}$

and volume?

build a pantograph

perspective drawing - Perspektive

hints


(c) 2019 sebastian.williams[at]sebinberlin.de - impressum und datenschutz - Powered by MathJax & XMin & HUGO & jsxgraph & mypaint