Author Nikolay Khyzhniak 
New mathematics is mathematics that is based on the laws of nature. Any physical law is an abstract mathematical law dressed in specific units of change. Mathematics is physics without clothes, physics is mathematics in clothes. Clothing (units of measurement) can be very different. Units of measurement are the key to understanding the laws of nature. Mathematics without units of measurement is an adult game of numbers according to the rules invented by mathematicians themselves. Today, mathematics is an ancient number game, similar to the game of chess, which adults play professionally. The mathematical theory of units of measurement, which will replace set theory in the future, has yet to be written.
All the secrets of the universe are written in the language of mathematics. If you want to understand math, always ask yourself the question: "How am I going to explain this to aliens?". This page contains links to my articles on mathematics, where I try to understand the answers to my questions. I get some kind of new mathematics, much wider and deeper than what we know. All these mathematical provisions and rules are not generally accepted, but reflect my personal view of mathematics.
Area of a trapezoid and division by zero.
Preprints of my article:

Number spirals introduction.
Number spirals.
Description of number spirals.
Analysis of number spirals.
Number spirals and numeral systems.
Number spirals and prime numbers.
 Permutation of terms in infinite sums (The Papers of Independent Authors. Volume 54. 2022 of p. 4143).
Mathematical operations with infinite series (The Papers of Independent Authors. Volume 54. 2022 of p. 4447).
Shift in arithmetic (The Papers of Independent Authors. Volume 57/ 2023 of p. 2223).
Sums classification (The Papers of Independent Authors. Volume 57.2023 of p. 2428).

Multiplication by zero.
Multiplication by zero and zero element.
Multiplication by zero in geometry.
Multiplication by zero in physics.
 Set theory.
Set and multiset.
Element of the set.
The formation of the set.
Set and subset.
Infinite set.
Measurement of plane angles (The Papers of Independent Authors. Volume 36 of p. 4345)
Trigonometric functions in a rectangle (The Papers of Independent Authors. Volume 36 of p. 4669)
 Trigonometric functions in a rectangle. Annotation. Short analysis of trigonometric functions.
Transformations of a triangle to a rectangle. Angular symmetry in a rectangle.
Three main types of trigonometric functions.
Terminating trigonometric functions.
The infinite trigonometric functions.
Quantity.
Variable units of measure.
Multiplication.
Examples of multiplication.
Distinctions between multiplication and addition.
Zero and infinity.
Decomposition on factors.
Division.
The linear angular functions.
Addition.
Decomposition on items. Closing part. Gratitude.
More deep consideration of bases of mathematics:
Why is a zero not a number?
Law of cosines for perimeter
Law of cosines in general
Bases of mathematics (The Papers of Independent Authors. Volume 19. 2011 of p. 7898)  under such name I wrote the cycle of reasons about mathematics, that is given below:
 basic axioms of mathematics
some concepts of mathematics
some concepts of mathematics are continuation
relativity is in mathematics
number line
relativity of concept is "Any Number"
units of measurements and mathematical actions
quantity as basis of mathematics
change of corner of scale
trigonometric dependences of corner of scale
space evolution
multiplication and division by zero
Natural numbers are determination  variation on a theme determination of natural numbers.
Integers determination  continuation of theme of mathematical determinations.