This creates an array of evenly distributed buttons that are sized and spaced such that the spacing + buttonWidth = 1.618*buttonWidth

golden ratio buttons

+ (NSArray *)evenlySpacedGoldenRatioButtonsWith:(NSInteger)numberOfButtons width:(CGFloat)spaceWidth yPos:(CGFloat)spaceHeight  {
    //this gives position in purely frame Math way
    //an autolayout method should be made -- trying to think how I want to implement that -- method that takes view and buttons -- block?
    
    CGFloat buttonWidth = spaceWidth/(1.303*(CGFloat)numberOfButtons + 0.3083);
    CGFloat buttonSpacing = 0.3083*buttonWidth;
    
    NSMutableArray *buttons = [NSMutableArray new];
    
    for (NSInteger i = 0; i < numberOfButtons; i++) {
        UIButton *aButton = [UIButton buttonWithType:UIButtonTypeCustom];
        CGFloat x = floor(buttonSpacing + (CGFloat)i*(buttonSpacing + buttonWidth));
        aButton.frame = CGRectMake(x, spaceHeight, buttonWidth, buttonWidth);
        
        //  Basic Default Colors
        aButton.backgroundColor = [UIColor darkGrayColor];
        [aButton setTitleColor:[UIColor whiteColor] forState:UIControlStateNormal];
        [aButton setTitleColor:[[UIColor whiteColor] colorWithAlphaComponent:.65] forState:UIControlStateHighlighted];
        
        [buttons addObject:aButton];
    }
    return [NSArray arrayWithArray:buttons];
}