should schools stop teaching the 3 4 5 triangle?

the most amazing thing i’ve ever experienced in my life is the 3 4 5 triangle

if you make a triangle with an angle that is EXACTLY 90 degrees with bases that are EXACTLY 3 and EXACTLY 4, the third side is not 4.99938347234234! the third side is not 5.0000000000078475345! the third side is not 5.0000000000000000000000000000000000000000000000000000000000010020023423! the third side is 5!!! 5.00000000000000000000000000000000000000000000000000000000000000000000000!!! 5!!!


this was true billions of years before any man ever existed

this is the mathematical truth of reality!

that’s the most unbelievable thing i’ve ever heard

i ain’t ever seen anything like that

the closest thing i’ve ever seen that even comes close to being that amazing is the 5 12 13 triangle

i should devote my entire life to the 3 4 5 triangle. i don’t know exactly what that means yet, but i should really do it

check out this. if you draw a square and mark the mid-points of the sides, you can make a 3 4 5 triangle!!

also, if you draw a perfect circle inside of the 3 4 5 triangle…

the radius of that circle…

is ONE!!!

i kid you not!


i don’t believe it.

i think it’s just made up.

i think they’re all lying.

the hypothenuse is actually 5.0000000000000000000000000000000000000106745 but nobody’s measured it that well yet. that’s what i think

don’t believe their lies. the 3 4 5 triangle is a myth that was formulated by a collaboration of mathematicians and clergymen thousands of years ago in order to try to prove that there is some sort of divinely organized structure to reality. but we all know that the chaotic nature of this universe would never actually have the 3rd side be EXACTLY 5. that is preposterous. that is an outrage!

when will modern mathematics quit accepting the 3 4 5 triangle lie that was spread through religious doctrine and perpetuated by christian society? when will the ugly truth be uncovered that the 3rd side is actually 5.0000000000000000000000000000000000000106745? if the scientific and mathematical community is supposed to be only based on unbiased measurements and logical empirical analysis, then why is the 3 4 5 triangle myth still accepted in 2009?

if our government allows this falsehood to be taught to our children in math class, then what’s next? teaching our children intelligent design in science class?

if they’re going to teach it to our children, they should at least emphasize that it is only an approximation and not exactly 5. giving the impression that the hypothenuse is exactly 5 influences kids to believe that there is a divinely organized structure to reality. religion should not be taught in public schools!

Their story seems to check out

the word you are looking for is “pythagorean”.
And excuse my ignorance about whatever the hell you are talking about, but does A^2+B^2 no longer equal C^2?

Toke jopic?

In a spatially curved universe. I think the OP thinks he’s making some sort of point about teaching Intelligent Design in public schools though.

Soooo many possible answers, but in the interest of keeping this thread in the Cartesian consensual reality, I’m gonna go with a classic:


measured what that well?

**This thread discusses the Pythagorean theorem, which assumes the sum of the squares of the legs of a right triangle is equal to the square of the remaining side. It is a theorem, not a fact, regarding non-collinear points on a unique plane. Because mathematicians still disagree over the details of Euclidean geometry, this material should be approached with an open mind, studied carefully, and critically considered. **

hmmmmm… Teach the controversy in math class?

I’ll make you a deal. You give me a triangle with one side EXACTLY 3 and one side EXACTLY 4 (with an EXACTLY 90 degree angle between them) and I promise to spare no expense in measuring the third side.

Well, from a measurement-error viewpoint, the OP is right about the fact that reality isn’t nice and clean like pure mathematics is. Empirically, sure, you’ll never find a true 3-4-5 triangle made by humans because even the most sophisticated equipment in the world, with the most exacting tolerances ever imposed, would still have some degree of error, although probably even less than what the OP lists as the “real” length of the hypotenuse. The 3-4-5 triangle, just like the circle, square, and any other mathematical shape is a purely theoretical construct that does not exist in reality. BUT…for all intents and purposes, we can use the theorems developed from these perfect shapes to great benefit, because they are beyond “good enough.”

Mathematics is only an approximation of reality, but it is a very good approximation, in fact, the best we can do. Our world is yet more complex than the most complex of predictive models, because of issues related to measurement (we can’t be accurate to infinite decimals) and knowledge (every single conceivable variable cannot be put into the model, because we simply don’t know what they all are and how they are related to one another). Yes, the 3-4-5 rule only applies to triangles that are axiomatically constructed, but for any real-world problem, that rule and others will work consistently, and thus predictably.

The same is true of the theory of evolution. As it stands, no, it is not 100% accurate, and it is far from complete. But it is a very good model (the best we have) for understanding the development of life, and its predictions are reasonably consistent and predictable.

There is a ‘triangle pose’ in yoga. It isn’t particularly hard either… to approximate. Funny though, I never seem to get quite into a right-angled triangle- it is always a little. bit. off.

Therefore the OP is correct. I have experienced it personally!


Non-Euclidean Geometry - they actually teach it in public schools.

Yeah, at the Boy’s Preparatory Academy of R’lyeh. What vast, loathsome shapes are these?!

Some would argue that the world is only an approximation of mathematics.

That’s my thought too.

I dispute this under the “infinite monkeys with infinite typewriters” theory ;).

There aren’t an infinite humans creating 3-4-5 triangles.
There aren’t an infinite yous trying to find the true 3-4-5 triangle.

Euclidian geometry is pretty well sorted. I can’t think of any issues that actually exist with it. But of course if you quuote Pythagoras, you need to preface that with “in a Euclidean space.” If you don’t, well it isn’t true. And we don’t live in a Euclidean world. If you get out a compas and measuring tape, and draw a nice triangle on the ground, it won’t be right. Worse, the bigger you make it the worse it will be.

Not only that, even if you try to get away from the surface of the shere we live on, you won’t find it easy to find any flat space. We live near gravitational bodies, and space is generally a bit warped. Even deep deep intergalactic space is not flat. The exact current theory on the nature of the universe varies a bit, but on the whole, the one thing that is pretty clear, it isn’t flat.

Of course the OP’s assertion that even in a Euclidian space the answer is 5.000…xxx is simply amusing. The deeper you look at the assertion, the more deep mathematics it violates. I would like to know what he has been smoking. Then I can avoid it. :smiley:

That’s not so amazing. You know what’s amazing? Grape Nuts cereal contains no grapes AND no nuts. Fight the power!

So, confission, I don’t know if this is an I.D. parody or what, but if you want it to stay open, you should explain what you’re driving at here.