Correct Formulations and Common Incorrect Formulations of The Pizza Constant

Correct Formulations and Common Incorrect Formulations of The Pizza Constant C.R. Kunferman October 2025 1 Introduction The wave curvature coined as ”the pizza constant” by the author has particular properties that are important in avoiding misinterpretation or reformulation of its structure which in its correct form produces very specific behavior. In this paper, the author and discoverer who calculated it shows a number of ways in which it is incorrectly formulated, exhibiting simple errors that will flatten and destroy the equations ability to produce useful results. It will be shown that when incorrectly formulated, or reduced by trigonometry, it becomes flat and no longer holds its form. The author further offers some additional valid ways of recreating it in computationally friendly formulations that uphold its value and prevent it from being reduced. Lastly a way to input variables into the equation, based on the limitations of its formulation that make it so unique, and so important as a causal governing wave curvature. 2 Abstract Many times in mathematics, we are driven to make certain assumptions and assertions to the reduction of equations which is by no means incorrect in the majority of the craft. However, when dealing with this particular curvature, it is important that these assumptions are not implemented, as to do so is to change the very basis of how it operates and will fundamentally alter the ways in which it interacts with other frameworks. What may initially appear as a simple construct is far more complex in its behavior than is readily visible, and by reducing it we essentially destroy the properties that make it work, showing us that it is somewhat fragile in the field of math, but moreover very defined, specific, constant, self-oscillating, and causal in the universe. 1 3 Incorrect Reductions 3.1 -1 The easiest and most common error with the constant is to reduce it to an equation that results in -1. This reduction removes half of the self-oscillating behavior and reduces it to a flat line, which will carry to any other calculations afterwards, removing any observable behavior to follow. A systematic collapse, no longer holding any more value than working with ”-1”. 3.2 cos2(t) Assumption: Simplifies mathematically to cos(2t), as −sin2t−cos2t=−cos(2t) and the denominator is always 1, so k(t) = −(−cos(2t)) = cos(2t) . In this example, the sin and cos are squared by an incorrect placement of the square before the t, resulting in an incorrect numerator and denominator. It is common practice to notate these in math as such and it many might argue that they are the same thing, however upon placing the values of t into the equations at a base level there is a fractional difference that looks small at a base level but becomes amplified and compounding as an error when scaled to cosmic levels. 3.3 A negative numerator In latex and in python a common mistake is placing the negative value inside the numerator making it −sin(t)2−cos(t)2˙ Combined with the above mistake: −sin2(t)−cos2(t) . Both will result in incorrect measurements and behavior of the wave curvature by themselves and in subsequent systems where it is used as input such as replacing lambda in general relativity. 3.4 Incorrect power in the denominator Common mistakes in the denominator include sin(t)2+(cos(t)2)3/2) , sin(t)2+ (cos(t)2)(3/2) , and sin(t)2+cos(t)(23/2) . In these examples we see that it doesn’t take much for a misplaced parentheses to unravel the denominator. When misapplied to the equation parentheses can easily encapsulate or delimit portions that will cause it to behave differently, mostly causing it to flatten or reduce to a constant value and losing its spiral, self-oscillating form. 3.5 Encapsulation by Parentheses In placing parentheses into the equation parts may become separated where there is no separation which can also result in failure. Common examples in error mainly occur in the denominator such as (sin(t)2) + (cos(t)2)(3/2) ˙ This example separates the (3/2) and only applies it to cos(t)2leaving sin(t)2on its own. Two additional parentheses are needed to encapsulate both parts of 2 the denominator in this case resulting in a slightly bloated version: ((sin(t)2)+ (cos(t)2))(3/2) ˙ For better formulation in this example it would be best to simply remove the two inner parentheses giving us (sin(t)2+cos(t)2)(3/2) ˙ When using in code it becomes important not to overlook a lack of parentheses in the denominator due to the manner it is processed. Example: (sin(t)2+cos(t)2)3/2˙ This example cubes the encapsulated values then divides it by 2 which becomes incorrect. Therefore it is good practice to keep the (3/2) within parentheses. 4 Correct Formulations 4.1 Negative for the whole equation as a function In the correct wave curvature the negative is placed outside of the entire equation, never inside. To always ensure the proper placement of this negative, we treat it as a function −() to begin or our proper formula. From this point all other operations will occur. 4.2 Numerator The correct numerator multiplies sine by incremental values of t, squares the result, then subtracts the squared multiplication of cosine values by increments of t. sin(t)2−cos(t)2 4.3 Denominator The correct denominator multiplies sine by incremental values of t, squares the result, then adds the squared multiplication of cosine values by increments of t. The result is then raised to the power of 3 divided by 2, or in decimal form one half of 3 equating to 1.5. (sin(t)2+cos(t)2)(3/2) Or (sin(t)2+cos(t)2)1.5 4.4 Complete Formula To now complete the formula, preparing it for insertion to code or latex correctly, we place the numerator and denominator into the −() −(sin(t)2−cos(t)2/(sin(t)2+cos(t)2)(3/2)) Or −(sin(t)2−cos(t)2/(sin(t)2+cos(t)2)1.5) With this formula complete one may now increment values of t and it will start to breath as it self-oscillates at values between 1 and -1. Correctly defined it is now ready for application as input, measurements and testing. 3 5 Alternatives for various purposes 5.1 Square Breaks The squares can be broken down to their underlying formulation to avoid mistakes in the placement of squaring. We break down the squared components as follows: sin(t)2= (sin(t)∗sin(t)) . By encapsulating it in a set of parentheses we isolate it in a modular form. The same is done with the cos(t)2components so that cos(t)2= (cos(t)∗ cos(t)) ˙ This gives our numerator the formulation (sin(t)∗sin(t))−(cos(t)∗cos(t)) . Our denominator is treated the same to become ((sin(t)∗sin(t)) + (cos(t)∗ cos(t))(3/2) 5.2 Correct Broken Square Formula −((sin(t)∗sin(t))−(cos(t)∗cos(t)))/((sin(t)∗sin(t))+(cos(t)∗cos(t)))(3/2)) 5.2.1 Broken Square (t) variables Because the wave curvature moves in all directions in time and space this may allow for the variation of time variables within the squaring but this has not been tested against observable data for confirmation. This would potentially provide up to 8 different values or ranges of t (t1,t2,t3,t4 etc). If each follows the incremental progression of time this may reveal how the wave interacts with itself at various points in its oscillating continuation. 6 Variable Version Along the lines of modulating the t variables within the curvature, we can place the sine and cosine functions into variables for targeted time interactions. 7 Correct Base Let a=sin(t) , b=cos(t) , c= 3/2=1.5 , and t=time to formulate k(t) = −(a2−b2/(a2+b2)c) or k(t) = −(((a∗a)−(b∗b))/((a∗a)+(b∗b))c) 8 Visual References for various correct applications The charts to follow were all produced using the equation in its correct form. They are provided for you to reference against your own to troubleshoot and look for possible discrepancies. 4 Figure 1: Pizza Constant Universal Density Over Time Figure 2: Pizza Constant Hubble Redshift Simulation 5 Figure 3: Pizza Constant with Matter in Universal Expansion Figure 4: Pizza Constant with Matter and Radiation 6 Figure 5: Pizza Constant Pressure Wave Lag Figure 6: Pizza Constant Time Lag 7 Figure 7: Pizza Constant Radiation Expansion 9 Conclusion It becomes clear that while in nature this wave curvature is robust and authoritative, And as we have been shown in this paper, when trying to compute it, it becomes fragile, and even sensitive to the slightest error. When formulated correctly it becomes immutable and constant, yet still very dynamic over time, nevertheless uninfluenced, and leading the way as it phases before all other waves. By preserving the spiral shape and self-oscillating nature of the wave curvature, we are still left with a bit of creativity to play with as variables and ranges to help us better understand reality as we stick our head outside the veil to see and learn how the gears of reality are turning. 8 Figure 8: 360 Degree by 2 degree Pizza Constant Ribbon Rotation Figure 9: 25 step of 7t ribbon rotation 9