bazylevnik0

crossection  2D plane(shape) with intersection of 3D shape(figure) - crosssection of solid Horizontal crossection Vertical crossection *of sphere **also exist different/other types of crossections(with random angles, complex planes) polyhedrons polygon - shape built by line segments Prism Based on an n-angle polygon, with two connected parallel bases *lines of connection are shaping parallelograms Formulas S(all) = 2*S(base)+ S(side) S(side) - n*shape V = S(of the base or horizontal crossection)*l *l - side edge *S - surface area *V - volume  Straight & regular prism Diagonal in straight: d = a^2*b^2*l^2, l = h *straigh with straigh angles to base Cube *all edges are equal Pyramid Straight and regular pyramid *in straight - top vertex above the centroid of the base Formulas S(all) = S(sides)+S(base) S(side) - S of triangle V = ⅓*S(base)*h *h - height **for proof V: Build cube with diagonals - will see 6 equal pyramids Volume of cube = a*b*c; S(base) = a*b; c = H In one pyr...

 spiral: https://en.wikipedia.org/wiki/Archimedean_spiral y=a+b*t t-represent time(angle) a,b -coefficients of shape https://www.shadertoy.com/view/mdBfD1 triangle: https://en.wikipedia.org/wiki/Sierpi%C5%84ski_triangle original algo: 1)draw triangle 2)split edges(equal) 3)connect triangle 4)move deep to the next triangle and repeat https://www.shadertoy.com/view/cd2fD1 set: https://en.wikipedia.org/wiki/Mandelbrot_set z(new)=z(old)^2+c (vector numbers) exist vizualization algorithms https://www.shadertoy.com/view/DsjBWw symmetry: *for set: https://www.shadertoy.com/view/DdjfRG exist two types:  algebraic(for example ^2) geometric(algebraic formula - a=|a|)

Planimetry  ( plane geometry) - shapes on plane Point and line basic geometrical shapes A not belong to a ( ); but B belong to a ( ); Two different lines isn’t crossing each other( parallels || ), or crossing in only one point *parallels in plane geometry  Line segment AB :  Ray: *AB & AC are additional to each other Two line segments are equal if they have the same length : Angle Angle ( 0, ab, AOB ):   Two angles are equal if they have an equal measure of angle(degree): Types of angles ab - acute angle ac - right angle ad - obtuse angle ae - straight angle * ab & ac - adjacent angles to each other  Vertical angles: * ab & b1a1 - equal and vertical a & b - perpendicular lines because c = 90 º Bisector of angle: ac = cb and c is bisector of ab Parallel lines a || b when 1 = 2 (or 3 = 4) * 1+ 3=180 º & 2+ 4=180 º ** if two lines parallel to third, then these two lines parallel to each other also Triangle Three points which not in one line ...