Define a Rational Triangle as a triangle in the Euclidean plane such that all three sides measured relative to each other are rational. Once, it was thought that all triangles were rational. The discovery of counterexamples is attributed to the Pythagoreans. Any triangle similar to a rational triangle is rational also. Take as a unit the greatest common measure of the three sides. Then the length of the sides are positive integers whose greatest common measure is unity. All rational triangles can be uniquely constructed in this way from three positive integers with greatest common divisor unity and each less than the sum of the other two (triangle inequality).

This triangle is obviously being 'irrational'...why do some things insist on being so difficult?

oh sweet datura, don't be so quick to call uppity at such traingle inequality. maybe there were obvious placed obstacles that continuously thwarted the efforts of a triangle such as this. could this not be true? poverty, triangular abuse, negative geometry self-talk that bordered on self-hate. maybe all the other triangles were just plain old-fashioned mean and our little triangle ate away at its heart, cut a little hole in his soul, or just blew his head off one day. my message is this, we dare not know the origins of such limitations of our supposed geometrically-challenged triangle.

lol...indeed i have underestimated the potential drama of the situation, and simply taken our triangles' mental health for granted...this is the best breakfast companion ever.

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The 'Rational' Triangle

Define a Rational Triangle as a triangle in the Euclidean plane such that all three sides measured relative to each other are rational. Once, it was thought that all triangles were rational. The discovery of counterexamples is attributed to the Pythagoreans. Any triangle similar to a rational triangle is rational also. Take as a unit the greatest common measure of the three sides. Then the length of the sides are positive integers whose greatest common measure is unity. All rational triangles can be uniquely constructed in this way from three positive integers with greatest common divisor unity and each less than the sum of the other two (triangle inequality).

This triangle is obviously being 'irrational'...why do some things insist on being so difficult?

next.

oh sweet datura, don't be so quick to call uppity at such traingle inequality. maybe there were obvious placed obstacles that continuously thwarted the efforts of a triangle such as this. could this not be true? poverty, triangular abuse, negative geometry self-talk that bordered on self-hate. maybe all the other triangles were just plain old-fashioned mean and our little triangle ate away at its heart, cut a little hole in his soul, or just blew his head off one day. my message is this, we dare not know the origins of such limitations of our supposed geometrically-challenged triangle.

it was probably just drugs though.

lol...indeed i have underestimated the potential drama of the situation, and simply taken our triangles' mental health for granted...this is the best breakfast companion ever.

...thats right, i said breakfast.

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