Moderator: Good afternoon. We have gathered the major definitions and theorems of triangles, the foundation of geometry, to hear their valuable opinions on the future of our planet from their unique perspectives.
I am the 'Basic Definition,' the beginning of everything. I come into existence only when three points are not on the same line. Sustainable development is the same. The three vertices of 'Economy,' 'Society,' and 'Environment' must not lie on the single straight line of 'short-term profit.' Only when these three support each other in balance can the stable figure of 'sustainability' be formed. We must redefine development itself. Not leaning towards one point, but pursuing a healthy space created by all three vertices—that is the basic principle I speak of.
I am 'Classification.' Whether by angles or sides, I clearly distinguish every triangle to reveal its nature. The Earth's problems also need clear 'classification.' Climate change is an urgent issue that has already crossed a dangerous threshold, like an 'obtuse triangle.' On the other hand, local community issues might be like an 'acute triangle,' still preventable and manageable. The solution must vary according to the nature of the problem. We need the wisdom to classify issues accurately by their urgency and characteristics, applying tailored solutions instead of lumping them all together as 'environmental problems.'
I am the 'Immutable Laws,' the basic properties. The sum of my interior angles is always 180°, and the sum of any two sides must always be greater than the third. The Earth has such absolute laws too, namely the 'finite total of resources.' The size of the triangle called Earth is fixed. No matter how large human desires (angles) grow, they cannot exceed 180°. And the development of two fields (sides) cannot come at the expense of the third (the environment). Sustainability is about abiding by the very conditions for a triangle's existence. If we ignore these basic laws, the triangle 'Earth' itself will collapse.
We are the 'Special Lines' that find the center of a triangle. The centroid, incenter, circumcenter, and orthocenter each find a point of balance in different ways. A sustainable society must also find all these 'four centers.' The 'centroid' is the point of equitable resource distribution. The 'incenter' is the core ethical value that all humanity must share. The 'circumcenter' is the center point of international cooperation where all nations participate. The 'orthocenter' is the point of insight that pierces through a problem vertically when a crisis hits. Only when these four centers are in harmony can the global community achieve a stable balance.
I am 'The Measure of Value,' the area formula. Whether calculated by base and height or by Heron's formula, I show the value of a triangle in numbers. Until now, we have used only one area formula: 'GDP.' By focusing only on the base (capital) and height (labor), we have ignored other important elements of the triangle. I propose a new 'sustainability area formula.' It must include the radius of the incircle (social trust), the radius of the circumcircle (international cooperation), and the harmony of the three sides (relationship with the environment). The values we pursue will only change when the way we measure them changes.
I am the 'Wisdom of Balance,' the properties of centers. Just as the centroid, incenter, circumcenter, and orthocenter all coincide in an equilateral triangle, the most ideal society is one where the centers of all values converge. Our society today is skewed towards the economic 'centroid,' causing the ethical 'incenter' and cooperative 'circumcenter' to be scattered. The farther these centers are from each other, the more unstable society becomes. The ultimate goal of sustainable development is to bring these four centers—economic, social, environmental, and ethical—as close as possible to a single point, thereby creating the most stable and harmonious 'equilateral triangle' social structure.
We are the 'Laws of Relationship,' the Law of Sines and Cosines. We show that no side or angle of a triangle exists in isolation; each is intricately connected to all other elements. The Earth system is the same. The destruction of the Amazon rainforest (side a) changes the climate on the other side of the planet (angle B), which in turn affects the marine ecosystem (side c). Like our laws, everything is connected. Sustainability starts from a deep understanding of this 'interdependence.' No nation can act alone for its own benefit; every policy must consider its impact on all other elements.
I am the 'Ideal Model,' the properties of special triangles. The equilateral triangle symbolizes perfect balance, while the right triangle represents a clear rule, the Pythagorean theorem. For sustainable development, we should strive for the ideal of the 'equilateral triangle'—a society where all nations and individuals have equal rights and responsibilities. Also, we must not forget the lesson of the 'right triangle.' We must keep in mind the 'Ecological Pythagorean Theorem': the sum of the squares of environmental destruction (base) and social conflict (height) equals the square of the disaster (hypotenuse) that future generations will have to bear. The cause and effect are clear.
I am 'Data-Driven Analysis,' the triangle on the coordinate plane. I transform all problems into specific coordinates and numbers for objective analysis. Sustainability is no longer an abstract discourse. We must plot the carbon emissions, resource consumption, and biodiversity index of each nation and city as precise (x, y) coordinates. Then, using the shoelace formula, we must calculate the 'area of impact' each region has on the environment. It is also necessary to identify where the 'centroid' of the problem lies, enabling data-driven policy decisions that concentrate resources and efforts on the most urgent and central areas.
We are 'Pattern Discovery and Scaling,' congruence and similarity. We study how to find successful models and apply or scale them elsewhere. The whole world does not need to invent a new solution simultaneously for sustainable development. Somewhere, a successful 'sustainable village' model (a single triangle) already exists. We must carefully analyze that successful case (the congruence conditions) and apply it to other regions through 'similarity transformation,' tailored to their specific characteristics. Finding small success stories and scaling up their patterns globally is the most realistic and efficient method of change.