Popular
 Women's measurements
 Big Mac
 Brain membranes
 The Number Three in American Culture
 Nina, Pinta, and the Santa Maria
 Three Furies
 How many triangles?
 Pythagoras  three is the perfect number
 Trinity symbol
 Simon Cowell: You Never Want The People That You Work With To Do Well
 Threes.com featured on the BBC2
 id, ego, superego
 Third Eye  Pineal Gland
 Featured Article  Allen H. Merriam
 Palaestrae
 Empirical rule  The 689599.7 Rule
 Three Foil Cross
 Three Holy sites of Islam
 Teeth
 Periodic Table  Law of Triads
How many triangles? 
Mathematics  
How many triangles are there in this picture? 94.7% of Americans miss the answer. Try it first, then see the answer below.
Answer: 6 small red triangles 3 small white triangles 3 medium red triangles with a small white triangle center 1 large triangle with 3 small triangles in the center  total = 13
Triangles within a TriangleDate: 11/10/96 at 07:38:57 From: Cato H. Jensen Subject: Geometry, Math Project (GCSE) 1996 This is an English project called "Triangles in Triangles" for I and H level. We are doing this in 10th grade. The question is: Investigate equilateral triangles of other sizes in order to examine the relationship between the size of a triangle and the total number of triangles it contains. The numbers (where n = total number of triangles and b = number of triangles in the base) given are : b n 1 1 2 5 3 13 4 27 5 48 6 78 7 118 8 170 I need to find a formula for the total number of triangles when there are X base triangles. I have done the rest of the project, but this part has gotten me really stuck. Date: 01/04/97 at 15:58:04 From: Doctor Chaos Subject: Re: Geometry, Math Project (GCSE) 1996 I think the best way to approach your problem is to examine the pattern you were given in order to calculate the total number of triangles. Look at these pictures: This triangle has 3 little triangles in the base so b=3. /\ In this triangle, there are nine (9) little /__\ triangles or b^2. Then there are three (3) /\ /\ triangles which are larger (containing 4 little ones) /__\/__\ and one (1) largest (containing all 9). /\ /\ /\ /__\/__\/__\ 9+3+1 = 13 triangles. This triangle has 4 little triangles in the base so b = 4. /\ The total of little triangles is b^2 or 16. /__\ The number of bigger triangles (containing 4 little /\ /\ ones) is 7. The number of still bigger triangles /__\/__\ (containing 9 little ones) is 3. The number of /\ /\ /\ largest triangles contains all 16 and is 1. /__\/__\/__\ /\ /\ /\ /\ 16+7+3+1 = 27 triangles /__\/__\/__\/__\ If we examine the numbers of triangles at every level, we may see a pattern which may then suggest a formula. b = Number of triangles in the base l = Number of little triangles f = Next largest triangle (contains 4) n = Next largest triangle (contains 9) s = Next largest triangle (contains 16) T = Total number of triangles b l f n s T 1 1 0 0 0 1 2 4 1 0 0 5 3 9 3 1 0 13 4 16 7 3 1 27 5 25 ? ? ? 48 6 36 ? ? ? 78 7 49 ? ? ? 118 8 64 ? ? ? 170 Organize the data you have already collected and see if there is a formula that will help you add up the various sizes of triangles to arrive at the total. You might even need 2 different formulas; one for an odd number on the base and one for even numbers. You never know until you try. Good luck. Doctor Chaos, The Math Forum Check out our web site! http://mathforum.org/dr.math/

Related Items
Quotation
George Bernard Shaw 
"Ptolemy created a universe that lasted a thousand years. Copernicus created a universe that lasted four hundred years. Einstein has created a universe, and I can't tell you how long it will last." 
3's flash
There are three ways to enter your thoughts into the Book of Threes. 1). You can join and request author rights by contacting us. 2). If you want to remain anonymous, log in with username: anonymous, and password: guest. 3). You can send us your ideas using Contact Us and we will enter the info for you. 