Basic Riddles – The start

Starting Triangle-Counting Riddles

My e-book “How to solve triangles counting riddles? ” startsmtpng2Small

with detailed explanation about triangles-counting method

and about symmetries. Then it deals with some basic shapes.

For instance the Scottish Square.ScottishSquare

How many triangles can you count in it?

It’s easy! Let’s sort & count them.

We can clearly see 4 simple triangles: A, B, C & D.ScottishSquare with ABCD

Each one of them is a quarter of the square.

But it’s not all. There are triangles which are made of 2 triangles adjacent to each other.

How many?  I can see 4 pairs of them. ScottishSquare with ABCD 4pairs

I used the letters to mark the basic ones and then count the bigger yellow ones:

A+B, A+C, D+B, D+C. That’s it!

Only 4 pairs are triangles. Look at it: The combination of B+C is not a triangle!

So, we discovered 4 triangles consisting of 2 basic triangles and the sum is:

4 basic triangles + 4 triangles consisting of 2 basic triangles = 4 + 4 = 8 triangles in total.

A whole chapter is dedicated to the multi-floor perfect triangles.

Yeah, the triangles which look like these:

Multi level triangles in a row

 

 

 

From left: 1-floor, 2-floors, 3-floors, 4-floors…

How many triangles can you count in each of them?

Can you find connections between the number of floors in such a triangle and the number of triangles you can find in it? Check it out…

Part A of the book deals with some more basic shapes.

Let’s look at some of the shapes:

Kite - basic shape

The Kite

 

 

Tringyטרינגי

Recty          Recty

 

 

The TrapezeTrapezGreen

 

The Pentagons

Three Pentagons - Small

 

 

and more…

How many triangles can you count in them?

You can use the triangles counting worksheets prepared for this mission…

An addition in 2017: a new shape which you can count it’s triangles.

It is The Crown

כתר

How many triangles can you count here?

Write your answer to the Triangelog…

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