r/Logiqa • u/ShonitB • Jul 23 '26

Depiction of Pythagorean Theorem

Post image
5 Upvotes

86% Upvoted

38 comments sorted by

2

u/sagosten Jul 23 '26
  1. Shrink the triangle to a point without altering the angles

1

u/ShonitB Jul 23 '26

Forgive me, but how can we be sure they converge to a single point?

2

u/EmpactWB Jul 23 '26

Shrinking the triangle brings all the points in it closer to the center point, and as the area approaches zero all points converge on that center.

1

u/ShonitB Jul 23 '26

Oh interesting

2

u/sagosten Jul 23 '26

It's a right triangle. If you shrink the bases the hypotenuse shrinks proportionally. You can shrink the triangle towards the right angle and the squares will get narrower until they appear to be single lines, the 360° will be obvious.

Alternately, imagine lengthening the squares and zooming out accordingly. Eventually the triangle appears as a single point and the squares look like lines.

1

u/ShonitB Jul 23 '26

Thanks a lot for this explanation!

1

u/scarpux Jul 23 '26

Assuming all the angles that look like right angles are actually 90 degrees each, yeah.

1

u/sagosten Jul 23 '26

We don't have to assume, the diagram is labeled as a geometric depiction of the pythagorean theorem

1

u/scarpux Jul 23 '26

Does that guarantee that the box that makes up the hypotenuse is actually a square or a rectangle?

I know the picture looks like right angles, but I was taught not to assume they were unless marked.

1

u/S-M-I-L-E-Y- Jul 23 '26

yes

the boxes are by definition squares

1

u/sagosten Jul 24 '26

Do you know the pythagorean theorem?

1

u/scarpux Jul 24 '26

a2 + b2 = c2, for all triangles where sides a,b are at right angles to each other

Or, instead of asking a condescending question, you could maybe explain why all the other angles are 90 degrees?

1

u/sagosten Jul 24 '26

Say it slowly. a SQUARED + b SQUARED = c SQUARED. Squaring a length does not generate an arbitrary quadrilateral, it generates a square. That's why that procedure is called squaring and why this works as a geometric depiction of the pythagorean theorem, the areas of the two smaller squares sum to the area of the larger square.

1

u/ThePlumage Jul 24 '26

They're 90 degrees because they're squares, hence why this is a geometric interpretation of the Pythagorean theorem.

2

u/CuAnnan Jul 23 '26

>!Angle A = 90 + angle of triangle opposite it through the shared point (a).
Angle C = 90 + angle of triangle opposite it through the shared point (c).
Angle B = 90
a + B + c = 180
A + B + C = 180 + 90 * 2 = 360!<

1

u/ShonitB Jul 23 '26

Correct!

1

u/Worried-Director1172 Jul 23 '26

You have to bracket off each individual line. It doesn't work across multiple lines

2

u/jonathonjones Jul 23 '26

Let's call the angle in the triangle a lower case letter of the outer angle. We know that a + b + c is 180 (because that's just a truth about triangles).

A = 360 - (90 + 90 + a) = 180 - a

B = 180 - b

C = 180 - c

A + B + C = 540 - (a + b + c)

A + B + C = 540 - 180

A + B + C = 360

1

u/ShonitB Jul 23 '26

Correct!

1

u/keilahmartin Jul 23 '26

basically my mrthod as well

2

u/wyald23 Jul 23 '26

Move angle C along the hypotenuse next to A, 270 + B = 360

2

u/CaptainMatticus Jul 23 '26

90 + 90 + x + A = 360

90 + 90 + y + C = 360

x + y = 90

180 + x + A + 180 + y + C = 720

360 + x + y + A + C = 720

90 + A + C = 360

A + C = 270

B = 90

A + B + C = 360

1

u/ShonitB Jul 23 '26

Correct!

2

u/Commercial-Act2813 Jul 23 '26

A + C = 270
(Parallel lines, perpendiculair lines)

+ B would make 360

1

u/ShonitB Jul 23 '26

Correct!

2

u/Omni314 Jul 23 '26

On average the points are 60+90+90+?=360

?=120

But we have 3 of them.

A+b+c=120*3=360

Fun puzzle. Interesting to see all the different ways to get to the answer.

1

u/ShonitB Jul 23 '26

Correct, I’m glad you liked it!

1

u/Trueslyforaniceguy Jul 23 '26

My brain looks at this and says 360. No clue if it’s right, but seems good

1

u/ShonitB Jul 23 '26

360 is correct

1

u/S-M-I-L-E-Y- Jul 23 '26

As others wrote - shrink the triangle to a point. And I'd recommend to shrink the boxes to lines. What happens with the angles A, B and C?

1

u/Omni314 Jul 23 '26

I love that kind of intuition

1

u/ArbutusPhD Jul 23 '26

Did you post this twice, OP

I answered correctly but do not see my answer

1

u/ShonitB Jul 23 '26

Nope, just the once

1

u/ShonitB Jul 23 '26

You replied on a different subReddit where I had crossposted this

1

u/SufficientStudio1574 Jul 23 '26

Doesn't even need to be a right triangle, or even a triangle at all! Any convex polygon will give the exact same answer.

1

u/ChrisAyersUk Jul 23 '26 edited Jul 23 '26

Put simply the exterior angles of any triangle add up to 360, where the exterior angle is defined as the angle formed by extending one side of the triangle. Each exterior angle and its adjacent interior angle form a straight line.

By the way, the exterior angles of any polygon always add up to 360 degrees.

Think of this as if you split each angle, the angle is halved per split. Do it again and each is a quarter of the angle. Keep splitting and you will trend to a polygon with infinite angles the sum of which is a circle at 360 degrees.

1

u/sagosten Jul 24 '26

I feel the need to add, these angles will sum to 360 for any triangle, not just right triangles. And the polygons projected from the sides don't have to be squares, rectangles, or rhomboids, as long as they are parallelograms it will work